Anhydrous α-D-Glucose (C$_{6}$H$_{12}$O$_{6}$) Structure: AB2C_oP96_19_6a_12a_6a-001
| Prototype | CH$_{2}$O |
| AFLOW prototype label | AB2C_oP96_19_6a_12a_6a-001 |
| Mineral name | α-D-glucose |
| CCDC | 1169299 |
| Pearson symbol | oP96 |
| Space group number | 19 |
| Space group symbol | $P2_12_12_1$ |
| AFLOW prototype command |
aflow --proto=AB2C_oP96_19_6a_12a_6a-001
--params=$a, \allowbreak b/a, \allowbreak c/a, \allowbreak x_{1}, \allowbreak y_{1}, \allowbreak z_{1}, \allowbreak x_{2}, \allowbreak y_{2}, \allowbreak z_{2}, \allowbreak x_{3}, \allowbreak y_{3}, \allowbreak z_{3}, \allowbreak x_{4}, \allowbreak y_{4}, \allowbreak z_{4}, \allowbreak x_{5}, \allowbreak y_{5}, \allowbreak z_{5}, \allowbreak x_{6}, \allowbreak y_{6}, \allowbreak z_{6}, \allowbreak x_{7}, \allowbreak y_{7}, \allowbreak z_{7}, \allowbreak x_{8}, \allowbreak y_{8}, \allowbreak z_{8}, \allowbreak x_{9}, \allowbreak y_{9}, \allowbreak z_{9}, \allowbreak x_{10}, \allowbreak y_{10}, \allowbreak z_{10}, \allowbreak x_{11}, \allowbreak y_{11}, \allowbreak z_{11}, \allowbreak x_{12}, \allowbreak y_{12}, \allowbreak z_{12}, \allowbreak x_{13}, \allowbreak y_{13}, \allowbreak z_{13}, \allowbreak x_{14}, \allowbreak y_{14}, \allowbreak z_{14}, \allowbreak x_{15}, \allowbreak y_{15}, \allowbreak z_{15}, \allowbreak x_{16}, \allowbreak y_{16}, \allowbreak z_{16}, \allowbreak x_{17}, \allowbreak y_{17}, \allowbreak z_{17}, \allowbreak x_{18}, \allowbreak y_{18}, \allowbreak z_{18}, \allowbreak x_{19}, \allowbreak y_{19}, \allowbreak z_{19}, \allowbreak x_{20}, \allowbreak y_{20}, \allowbreak z_{20}, \allowbreak x_{21}, \allowbreak y_{21}, \allowbreak z_{21}, \allowbreak x_{22}, \allowbreak y_{22}, \allowbreak z_{22}, \allowbreak x_{23}, \allowbreak y_{23}, \allowbreak z_{23}, \allowbreak x_{24}, \allowbreak y_{24}, \allowbreak z_{24}$ |
- Anhydrous glucose can be found in nature in two forms:
- $\alpha$-D-glucose (this structure),
- $\beta$-D-glucose and
- $\alpha$-D-glucose monohydrate.
- This is a chiral compound.
- The
D
indicates that a solution of this form of glucose will rotate polarized light to the right, while theL
type rotates light to the left. - Only D-glucose is found in nature, but the L-type can be synthesized.
- As $\alpha$-L-glucose is the enantiomer of $\alpha$-D-glucose its structure should be a mirror image of this one, but we have not been able to find a report of its structure.
- $\alpha$- and $\beta$-D-glucose have the same AFLOW prototype label, AB2C_oP96_19_6a_12a_6a. They are generated by the same symmetry operations with different sets of parameters (
--params) specified in their corresponding CIF files.
\[ \begin{array}{ccc}
\mathbf{a_{1}}&=&a \,\mathbf{\hat{x}}\\\mathbf{a_{2}}&=&b \,\mathbf{\hat{y}}\\\mathbf{a_{3}}&=&c \,\mathbf{\hat{z}}
\end{array}\]
Basis vectors
| Lattice coordinates | Cartesian coordinates | Wyckoff position | Atom type | |||
|---|---|---|---|---|---|---|
| $\mathbf{B_{1}}$ | = | $x_{1} \, \mathbf{a}_{1}+y_{1} \, \mathbf{a}_{2}+z_{1} \, \mathbf{a}_{3}$ | = | $a x_{1} \,\mathbf{\hat{x}}+b y_{1} \,\mathbf{\hat{y}}+c z_{1} \,\mathbf{\hat{z}}$ | (4a) | C I |
| $\mathbf{B_{2}}$ | = | $- \left(x_{1} - \frac{1}{2}\right) \, \mathbf{a}_{1}- y_{1} \, \mathbf{a}_{2}+\left(z_{1} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- a \left(x_{1} - \frac{1}{2}\right) \,\mathbf{\hat{x}}- b y_{1} \,\mathbf{\hat{y}}+c \left(z_{1} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (4a) | C I |
| $\mathbf{B_{3}}$ | = | $- x_{1} \, \mathbf{a}_{1}+\left(y_{1} + \frac{1}{2}\right) \, \mathbf{a}_{2}- \left(z_{1} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- a x_{1} \,\mathbf{\hat{x}}+b \left(y_{1} + \frac{1}{2}\right) \,\mathbf{\hat{y}}- c \left(z_{1} - \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (4a) | C I |
| $\mathbf{B_{4}}$ | = | $\left(x_{1} + \frac{1}{2}\right) \, \mathbf{a}_{1}- \left(y_{1} - \frac{1}{2}\right) \, \mathbf{a}_{2}- z_{1} \, \mathbf{a}_{3}$ | = | $a \left(x_{1} + \frac{1}{2}\right) \,\mathbf{\hat{x}}- b \left(y_{1} - \frac{1}{2}\right) \,\mathbf{\hat{y}}- c z_{1} \,\mathbf{\hat{z}}$ | (4a) | C I |
| $\mathbf{B_{5}}$ | = | $x_{2} \, \mathbf{a}_{1}+y_{2} \, \mathbf{a}_{2}+z_{2} \, \mathbf{a}_{3}$ | = | $a x_{2} \,\mathbf{\hat{x}}+b y_{2} \,\mathbf{\hat{y}}+c z_{2} \,\mathbf{\hat{z}}$ | (4a) | C II |
| $\mathbf{B_{6}}$ | = | $- \left(x_{2} - \frac{1}{2}\right) \, \mathbf{a}_{1}- y_{2} \, \mathbf{a}_{2}+\left(z_{2} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- a \left(x_{2} - \frac{1}{2}\right) \,\mathbf{\hat{x}}- b y_{2} \,\mathbf{\hat{y}}+c \left(z_{2} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (4a) | C II |
| $\mathbf{B_{7}}$ | = | $- x_{2} \, \mathbf{a}_{1}+\left(y_{2} + \frac{1}{2}\right) \, \mathbf{a}_{2}- \left(z_{2} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- a x_{2} \,\mathbf{\hat{x}}+b \left(y_{2} + \frac{1}{2}\right) \,\mathbf{\hat{y}}- c \left(z_{2} - \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (4a) | C II |
| $\mathbf{B_{8}}$ | = | $\left(x_{2} + \frac{1}{2}\right) \, \mathbf{a}_{1}- \left(y_{2} - \frac{1}{2}\right) \, \mathbf{a}_{2}- z_{2} \, \mathbf{a}_{3}$ | = | $a \left(x_{2} + \frac{1}{2}\right) \,\mathbf{\hat{x}}- b \left(y_{2} - \frac{1}{2}\right) \,\mathbf{\hat{y}}- c z_{2} \,\mathbf{\hat{z}}$ | (4a) | C II |
| $\mathbf{B_{9}}$ | = | $x_{3} \, \mathbf{a}_{1}+y_{3} \, \mathbf{a}_{2}+z_{3} \, \mathbf{a}_{3}$ | = | $a x_{3} \,\mathbf{\hat{x}}+b y_{3} \,\mathbf{\hat{y}}+c z_{3} \,\mathbf{\hat{z}}$ | (4a) | C III |
| $\mathbf{B_{10}}$ | = | $- \left(x_{3} - \frac{1}{2}\right) \, \mathbf{a}_{1}- y_{3} \, \mathbf{a}_{2}+\left(z_{3} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- a \left(x_{3} - \frac{1}{2}\right) \,\mathbf{\hat{x}}- b y_{3} \,\mathbf{\hat{y}}+c \left(z_{3} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (4a) | C III |
| $\mathbf{B_{11}}$ | = | $- x_{3} \, \mathbf{a}_{1}+\left(y_{3} + \frac{1}{2}\right) \, \mathbf{a}_{2}- \left(z_{3} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- a x_{3} \,\mathbf{\hat{x}}+b \left(y_{3} + \frac{1}{2}\right) \,\mathbf{\hat{y}}- c \left(z_{3} - \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (4a) | C III |
| $\mathbf{B_{12}}$ | = | $\left(x_{3} + \frac{1}{2}\right) \, \mathbf{a}_{1}- \left(y_{3} - \frac{1}{2}\right) \, \mathbf{a}_{2}- z_{3} \, \mathbf{a}_{3}$ | = | $a \left(x_{3} + \frac{1}{2}\right) \,\mathbf{\hat{x}}- b \left(y_{3} - \frac{1}{2}\right) \,\mathbf{\hat{y}}- c z_{3} \,\mathbf{\hat{z}}$ | (4a) | C III |
| $\mathbf{B_{13}}$ | = | $x_{4} \, \mathbf{a}_{1}+y_{4} \, \mathbf{a}_{2}+z_{4} \, \mathbf{a}_{3}$ | = | $a x_{4} \,\mathbf{\hat{x}}+b y_{4} \,\mathbf{\hat{y}}+c z_{4} \,\mathbf{\hat{z}}$ | (4a) | C IV |
| $\mathbf{B_{14}}$ | = | $- \left(x_{4} - \frac{1}{2}\right) \, \mathbf{a}_{1}- y_{4} \, \mathbf{a}_{2}+\left(z_{4} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- a \left(x_{4} - \frac{1}{2}\right) \,\mathbf{\hat{x}}- b y_{4} \,\mathbf{\hat{y}}+c \left(z_{4} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (4a) | C IV |
| $\mathbf{B_{15}}$ | = | $- x_{4} \, \mathbf{a}_{1}+\left(y_{4} + \frac{1}{2}\right) \, \mathbf{a}_{2}- \left(z_{4} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- a x_{4} \,\mathbf{\hat{x}}+b \left(y_{4} + \frac{1}{2}\right) \,\mathbf{\hat{y}}- c \left(z_{4} - \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (4a) | C IV |
| $\mathbf{B_{16}}$ | = | $\left(x_{4} + \frac{1}{2}\right) \, \mathbf{a}_{1}- \left(y_{4} - \frac{1}{2}\right) \, \mathbf{a}_{2}- z_{4} \, \mathbf{a}_{3}$ | = | $a \left(x_{4} + \frac{1}{2}\right) \,\mathbf{\hat{x}}- b \left(y_{4} - \frac{1}{2}\right) \,\mathbf{\hat{y}}- c z_{4} \,\mathbf{\hat{z}}$ | (4a) | C IV |
| $\mathbf{B_{17}}$ | = | $x_{5} \, \mathbf{a}_{1}+y_{5} \, \mathbf{a}_{2}+z_{5} \, \mathbf{a}_{3}$ | = | $a x_{5} \,\mathbf{\hat{x}}+b y_{5} \,\mathbf{\hat{y}}+c z_{5} \,\mathbf{\hat{z}}$ | (4a) | C V |
| $\mathbf{B_{18}}$ | = | $- \left(x_{5} - \frac{1}{2}\right) \, \mathbf{a}_{1}- y_{5} \, \mathbf{a}_{2}+\left(z_{5} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- a \left(x_{5} - \frac{1}{2}\right) \,\mathbf{\hat{x}}- b y_{5} \,\mathbf{\hat{y}}+c \left(z_{5} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (4a) | C V |
| $\mathbf{B_{19}}$ | = | $- x_{5} \, \mathbf{a}_{1}+\left(y_{5} + \frac{1}{2}\right) \, \mathbf{a}_{2}- \left(z_{5} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- a x_{5} \,\mathbf{\hat{x}}+b \left(y_{5} + \frac{1}{2}\right) \,\mathbf{\hat{y}}- c \left(z_{5} - \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (4a) | C V |
| $\mathbf{B_{20}}$ | = | $\left(x_{5} + \frac{1}{2}\right) \, \mathbf{a}_{1}- \left(y_{5} - \frac{1}{2}\right) \, \mathbf{a}_{2}- z_{5} \, \mathbf{a}_{3}$ | = | $a \left(x_{5} + \frac{1}{2}\right) \,\mathbf{\hat{x}}- b \left(y_{5} - \frac{1}{2}\right) \,\mathbf{\hat{y}}- c z_{5} \,\mathbf{\hat{z}}$ | (4a) | C V |
| $\mathbf{B_{21}}$ | = | $x_{6} \, \mathbf{a}_{1}+y_{6} \, \mathbf{a}_{2}+z_{6} \, \mathbf{a}_{3}$ | = | $a x_{6} \,\mathbf{\hat{x}}+b y_{6} \,\mathbf{\hat{y}}+c z_{6} \,\mathbf{\hat{z}}$ | (4a) | C VI |
| $\mathbf{B_{22}}$ | = | $- \left(x_{6} - \frac{1}{2}\right) \, \mathbf{a}_{1}- y_{6} \, \mathbf{a}_{2}+\left(z_{6} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- a \left(x_{6} - \frac{1}{2}\right) \,\mathbf{\hat{x}}- b y_{6} \,\mathbf{\hat{y}}+c \left(z_{6} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (4a) | C VI |
| $\mathbf{B_{23}}$ | = | $- x_{6} \, \mathbf{a}_{1}+\left(y_{6} + \frac{1}{2}\right) \, \mathbf{a}_{2}- \left(z_{6} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- a x_{6} \,\mathbf{\hat{x}}+b \left(y_{6} + \frac{1}{2}\right) \,\mathbf{\hat{y}}- c \left(z_{6} - \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (4a) | C VI |
| $\mathbf{B_{24}}$ | = | $\left(x_{6} + \frac{1}{2}\right) \, \mathbf{a}_{1}- \left(y_{6} - \frac{1}{2}\right) \, \mathbf{a}_{2}- z_{6} \, \mathbf{a}_{3}$ | = | $a \left(x_{6} + \frac{1}{2}\right) \,\mathbf{\hat{x}}- b \left(y_{6} - \frac{1}{2}\right) \,\mathbf{\hat{y}}- c z_{6} \,\mathbf{\hat{z}}$ | (4a) | C VI |
| $\mathbf{B_{25}}$ | = | $x_{7} \, \mathbf{a}_{1}+y_{7} \, \mathbf{a}_{2}+z_{7} \, \mathbf{a}_{3}$ | = | $a x_{7} \,\mathbf{\hat{x}}+b y_{7} \,\mathbf{\hat{y}}+c z_{7} \,\mathbf{\hat{z}}$ | (4a) | H I |
| $\mathbf{B_{26}}$ | = | $- \left(x_{7} - \frac{1}{2}\right) \, \mathbf{a}_{1}- y_{7} \, \mathbf{a}_{2}+\left(z_{7} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- a \left(x_{7} - \frac{1}{2}\right) \,\mathbf{\hat{x}}- b y_{7} \,\mathbf{\hat{y}}+c \left(z_{7} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (4a) | H I |
| $\mathbf{B_{27}}$ | = | $- x_{7} \, \mathbf{a}_{1}+\left(y_{7} + \frac{1}{2}\right) \, \mathbf{a}_{2}- \left(z_{7} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- a x_{7} \,\mathbf{\hat{x}}+b \left(y_{7} + \frac{1}{2}\right) \,\mathbf{\hat{y}}- c \left(z_{7} - \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (4a) | H I |
| $\mathbf{B_{28}}$ | = | $\left(x_{7} + \frac{1}{2}\right) \, \mathbf{a}_{1}- \left(y_{7} - \frac{1}{2}\right) \, \mathbf{a}_{2}- z_{7} \, \mathbf{a}_{3}$ | = | $a \left(x_{7} + \frac{1}{2}\right) \,\mathbf{\hat{x}}- b \left(y_{7} - \frac{1}{2}\right) \,\mathbf{\hat{y}}- c z_{7} \,\mathbf{\hat{z}}$ | (4a) | H I |
| $\mathbf{B_{29}}$ | = | $x_{8} \, \mathbf{a}_{1}+y_{8} \, \mathbf{a}_{2}+z_{8} \, \mathbf{a}_{3}$ | = | $a x_{8} \,\mathbf{\hat{x}}+b y_{8} \,\mathbf{\hat{y}}+c z_{8} \,\mathbf{\hat{z}}$ | (4a) | H II |
| $\mathbf{B_{30}}$ | = | $- \left(x_{8} - \frac{1}{2}\right) \, \mathbf{a}_{1}- y_{8} \, \mathbf{a}_{2}+\left(z_{8} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- a \left(x_{8} - \frac{1}{2}\right) \,\mathbf{\hat{x}}- b y_{8} \,\mathbf{\hat{y}}+c \left(z_{8} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (4a) | H II |
| $\mathbf{B_{31}}$ | = | $- x_{8} \, \mathbf{a}_{1}+\left(y_{8} + \frac{1}{2}\right) \, \mathbf{a}_{2}- \left(z_{8} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- a x_{8} \,\mathbf{\hat{x}}+b \left(y_{8} + \frac{1}{2}\right) \,\mathbf{\hat{y}}- c \left(z_{8} - \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (4a) | H II |
| $\mathbf{B_{32}}$ | = | $\left(x_{8} + \frac{1}{2}\right) \, \mathbf{a}_{1}- \left(y_{8} - \frac{1}{2}\right) \, \mathbf{a}_{2}- z_{8} \, \mathbf{a}_{3}$ | = | $a \left(x_{8} + \frac{1}{2}\right) \,\mathbf{\hat{x}}- b \left(y_{8} - \frac{1}{2}\right) \,\mathbf{\hat{y}}- c z_{8} \,\mathbf{\hat{z}}$ | (4a) | H II |
| $\mathbf{B_{33}}$ | = | $x_{9} \, \mathbf{a}_{1}+y_{9} \, \mathbf{a}_{2}+z_{9} \, \mathbf{a}_{3}$ | = | $a x_{9} \,\mathbf{\hat{x}}+b y_{9} \,\mathbf{\hat{y}}+c z_{9} \,\mathbf{\hat{z}}$ | (4a) | H III |
| $\mathbf{B_{34}}$ | = | $- \left(x_{9} - \frac{1}{2}\right) \, \mathbf{a}_{1}- y_{9} \, \mathbf{a}_{2}+\left(z_{9} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- a \left(x_{9} - \frac{1}{2}\right) \,\mathbf{\hat{x}}- b y_{9} \,\mathbf{\hat{y}}+c \left(z_{9} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (4a) | H III |
| $\mathbf{B_{35}}$ | = | $- x_{9} \, \mathbf{a}_{1}+\left(y_{9} + \frac{1}{2}\right) \, \mathbf{a}_{2}- \left(z_{9} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- a x_{9} \,\mathbf{\hat{x}}+b \left(y_{9} + \frac{1}{2}\right) \,\mathbf{\hat{y}}- c \left(z_{9} - \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (4a) | H III |
| $\mathbf{B_{36}}$ | = | $\left(x_{9} + \frac{1}{2}\right) \, \mathbf{a}_{1}- \left(y_{9} - \frac{1}{2}\right) \, \mathbf{a}_{2}- z_{9} \, \mathbf{a}_{3}$ | = | $a \left(x_{9} + \frac{1}{2}\right) \,\mathbf{\hat{x}}- b \left(y_{9} - \frac{1}{2}\right) \,\mathbf{\hat{y}}- c z_{9} \,\mathbf{\hat{z}}$ | (4a) | H III |
| $\mathbf{B_{37}}$ | = | $x_{10} \, \mathbf{a}_{1}+y_{10} \, \mathbf{a}_{2}+z_{10} \, \mathbf{a}_{3}$ | = | $a x_{10} \,\mathbf{\hat{x}}+b y_{10} \,\mathbf{\hat{y}}+c z_{10} \,\mathbf{\hat{z}}$ | (4a) | H IV |
| $\mathbf{B_{38}}$ | = | $- \left(x_{10} - \frac{1}{2}\right) \, \mathbf{a}_{1}- y_{10} \, \mathbf{a}_{2}+\left(z_{10} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- a \left(x_{10} - \frac{1}{2}\right) \,\mathbf{\hat{x}}- b y_{10} \,\mathbf{\hat{y}}+c \left(z_{10} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (4a) | H IV |
| $\mathbf{B_{39}}$ | = | $- x_{10} \, \mathbf{a}_{1}+\left(y_{10} + \frac{1}{2}\right) \, \mathbf{a}_{2}- \left(z_{10} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- a x_{10} \,\mathbf{\hat{x}}+b \left(y_{10} + \frac{1}{2}\right) \,\mathbf{\hat{y}}- c \left(z_{10} - \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (4a) | H IV |
| $\mathbf{B_{40}}$ | = | $\left(x_{10} + \frac{1}{2}\right) \, \mathbf{a}_{1}- \left(y_{10} - \frac{1}{2}\right) \, \mathbf{a}_{2}- z_{10} \, \mathbf{a}_{3}$ | = | $a \left(x_{10} + \frac{1}{2}\right) \,\mathbf{\hat{x}}- b \left(y_{10} - \frac{1}{2}\right) \,\mathbf{\hat{y}}- c z_{10} \,\mathbf{\hat{z}}$ | (4a) | H IV |
| $\mathbf{B_{41}}$ | = | $x_{11} \, \mathbf{a}_{1}+y_{11} \, \mathbf{a}_{2}+z_{11} \, \mathbf{a}_{3}$ | = | $a x_{11} \,\mathbf{\hat{x}}+b y_{11} \,\mathbf{\hat{y}}+c z_{11} \,\mathbf{\hat{z}}$ | (4a) | H V |
| $\mathbf{B_{42}}$ | = | $- \left(x_{11} - \frac{1}{2}\right) \, \mathbf{a}_{1}- y_{11} \, \mathbf{a}_{2}+\left(z_{11} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- a \left(x_{11} - \frac{1}{2}\right) \,\mathbf{\hat{x}}- b y_{11} \,\mathbf{\hat{y}}+c \left(z_{11} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (4a) | H V |
| $\mathbf{B_{43}}$ | = | $- x_{11} \, \mathbf{a}_{1}+\left(y_{11} + \frac{1}{2}\right) \, \mathbf{a}_{2}- \left(z_{11} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- a x_{11} \,\mathbf{\hat{x}}+b \left(y_{11} + \frac{1}{2}\right) \,\mathbf{\hat{y}}- c \left(z_{11} - \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (4a) | H V |
| $\mathbf{B_{44}}$ | = | $\left(x_{11} + \frac{1}{2}\right) \, \mathbf{a}_{1}- \left(y_{11} - \frac{1}{2}\right) \, \mathbf{a}_{2}- z_{11} \, \mathbf{a}_{3}$ | = | $a \left(x_{11} + \frac{1}{2}\right) \,\mathbf{\hat{x}}- b \left(y_{11} - \frac{1}{2}\right) \,\mathbf{\hat{y}}- c z_{11} \,\mathbf{\hat{z}}$ | (4a) | H V |
| $\mathbf{B_{45}}$ | = | $x_{12} \, \mathbf{a}_{1}+y_{12} \, \mathbf{a}_{2}+z_{12} \, \mathbf{a}_{3}$ | = | $a x_{12} \,\mathbf{\hat{x}}+b y_{12} \,\mathbf{\hat{y}}+c z_{12} \,\mathbf{\hat{z}}$ | (4a) | H VI |
| $\mathbf{B_{46}}$ | = | $- \left(x_{12} - \frac{1}{2}\right) \, \mathbf{a}_{1}- y_{12} \, \mathbf{a}_{2}+\left(z_{12} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- a \left(x_{12} - \frac{1}{2}\right) \,\mathbf{\hat{x}}- b y_{12} \,\mathbf{\hat{y}}+c \left(z_{12} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (4a) | H VI |
| $\mathbf{B_{47}}$ | = | $- x_{12} \, \mathbf{a}_{1}+\left(y_{12} + \frac{1}{2}\right) \, \mathbf{a}_{2}- \left(z_{12} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- a x_{12} \,\mathbf{\hat{x}}+b \left(y_{12} + \frac{1}{2}\right) \,\mathbf{\hat{y}}- c \left(z_{12} - \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (4a) | H VI |
| $\mathbf{B_{48}}$ | = | $\left(x_{12} + \frac{1}{2}\right) \, \mathbf{a}_{1}- \left(y_{12} - \frac{1}{2}\right) \, \mathbf{a}_{2}- z_{12} \, \mathbf{a}_{3}$ | = | $a \left(x_{12} + \frac{1}{2}\right) \,\mathbf{\hat{x}}- b \left(y_{12} - \frac{1}{2}\right) \,\mathbf{\hat{y}}- c z_{12} \,\mathbf{\hat{z}}$ | (4a) | H VI |
| $\mathbf{B_{49}}$ | = | $x_{13} \, \mathbf{a}_{1}+y_{13} \, \mathbf{a}_{2}+z_{13} \, \mathbf{a}_{3}$ | = | $a x_{13} \,\mathbf{\hat{x}}+b y_{13} \,\mathbf{\hat{y}}+c z_{13} \,\mathbf{\hat{z}}$ | (4a) | H VII |
| $\mathbf{B_{50}}$ | = | $- \left(x_{13} - \frac{1}{2}\right) \, \mathbf{a}_{1}- y_{13} \, \mathbf{a}_{2}+\left(z_{13} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- a \left(x_{13} - \frac{1}{2}\right) \,\mathbf{\hat{x}}- b y_{13} \,\mathbf{\hat{y}}+c \left(z_{13} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (4a) | H VII |
| $\mathbf{B_{51}}$ | = | $- x_{13} \, \mathbf{a}_{1}+\left(y_{13} + \frac{1}{2}\right) \, \mathbf{a}_{2}- \left(z_{13} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- a x_{13} \,\mathbf{\hat{x}}+b \left(y_{13} + \frac{1}{2}\right) \,\mathbf{\hat{y}}- c \left(z_{13} - \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (4a) | H VII |
| $\mathbf{B_{52}}$ | = | $\left(x_{13} + \frac{1}{2}\right) \, \mathbf{a}_{1}- \left(y_{13} - \frac{1}{2}\right) \, \mathbf{a}_{2}- z_{13} \, \mathbf{a}_{3}$ | = | $a \left(x_{13} + \frac{1}{2}\right) \,\mathbf{\hat{x}}- b \left(y_{13} - \frac{1}{2}\right) \,\mathbf{\hat{y}}- c z_{13} \,\mathbf{\hat{z}}$ | (4a) | H VII |
| $\mathbf{B_{53}}$ | = | $x_{14} \, \mathbf{a}_{1}+y_{14} \, \mathbf{a}_{2}+z_{14} \, \mathbf{a}_{3}$ | = | $a x_{14} \,\mathbf{\hat{x}}+b y_{14} \,\mathbf{\hat{y}}+c z_{14} \,\mathbf{\hat{z}}$ | (4a) | H VIII |
| $\mathbf{B_{54}}$ | = | $- \left(x_{14} - \frac{1}{2}\right) \, \mathbf{a}_{1}- y_{14} \, \mathbf{a}_{2}+\left(z_{14} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- a \left(x_{14} - \frac{1}{2}\right) \,\mathbf{\hat{x}}- b y_{14} \,\mathbf{\hat{y}}+c \left(z_{14} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (4a) | H VIII |
| $\mathbf{B_{55}}$ | = | $- x_{14} \, \mathbf{a}_{1}+\left(y_{14} + \frac{1}{2}\right) \, \mathbf{a}_{2}- \left(z_{14} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- a x_{14} \,\mathbf{\hat{x}}+b \left(y_{14} + \frac{1}{2}\right) \,\mathbf{\hat{y}}- c \left(z_{14} - \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (4a) | H VIII |
| $\mathbf{B_{56}}$ | = | $\left(x_{14} + \frac{1}{2}\right) \, \mathbf{a}_{1}- \left(y_{14} - \frac{1}{2}\right) \, \mathbf{a}_{2}- z_{14} \, \mathbf{a}_{3}$ | = | $a \left(x_{14} + \frac{1}{2}\right) \,\mathbf{\hat{x}}- b \left(y_{14} - \frac{1}{2}\right) \,\mathbf{\hat{y}}- c z_{14} \,\mathbf{\hat{z}}$ | (4a) | H VIII |
| $\mathbf{B_{57}}$ | = | $x_{15} \, \mathbf{a}_{1}+y_{15} \, \mathbf{a}_{2}+z_{15} \, \mathbf{a}_{3}$ | = | $a x_{15} \,\mathbf{\hat{x}}+b y_{15} \,\mathbf{\hat{y}}+c z_{15} \,\mathbf{\hat{z}}$ | (4a) | H IX |
| $\mathbf{B_{58}}$ | = | $- \left(x_{15} - \frac{1}{2}\right) \, \mathbf{a}_{1}- y_{15} \, \mathbf{a}_{2}+\left(z_{15} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- a \left(x_{15} - \frac{1}{2}\right) \,\mathbf{\hat{x}}- b y_{15} \,\mathbf{\hat{y}}+c \left(z_{15} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (4a) | H IX |
| $\mathbf{B_{59}}$ | = | $- x_{15} \, \mathbf{a}_{1}+\left(y_{15} + \frac{1}{2}\right) \, \mathbf{a}_{2}- \left(z_{15} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- a x_{15} \,\mathbf{\hat{x}}+b \left(y_{15} + \frac{1}{2}\right) \,\mathbf{\hat{y}}- c \left(z_{15} - \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (4a) | H IX |
| $\mathbf{B_{60}}$ | = | $\left(x_{15} + \frac{1}{2}\right) \, \mathbf{a}_{1}- \left(y_{15} - \frac{1}{2}\right) \, \mathbf{a}_{2}- z_{15} \, \mathbf{a}_{3}$ | = | $a \left(x_{15} + \frac{1}{2}\right) \,\mathbf{\hat{x}}- b \left(y_{15} - \frac{1}{2}\right) \,\mathbf{\hat{y}}- c z_{15} \,\mathbf{\hat{z}}$ | (4a) | H IX |
| $\mathbf{B_{61}}$ | = | $x_{16} \, \mathbf{a}_{1}+y_{16} \, \mathbf{a}_{2}+z_{16} \, \mathbf{a}_{3}$ | = | $a x_{16} \,\mathbf{\hat{x}}+b y_{16} \,\mathbf{\hat{y}}+c z_{16} \,\mathbf{\hat{z}}$ | (4a) | H X |
| $\mathbf{B_{62}}$ | = | $- \left(x_{16} - \frac{1}{2}\right) \, \mathbf{a}_{1}- y_{16} \, \mathbf{a}_{2}+\left(z_{16} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- a \left(x_{16} - \frac{1}{2}\right) \,\mathbf{\hat{x}}- b y_{16} \,\mathbf{\hat{y}}+c \left(z_{16} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (4a) | H X |
| $\mathbf{B_{63}}$ | = | $- x_{16} \, \mathbf{a}_{1}+\left(y_{16} + \frac{1}{2}\right) \, \mathbf{a}_{2}- \left(z_{16} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- a x_{16} \,\mathbf{\hat{x}}+b \left(y_{16} + \frac{1}{2}\right) \,\mathbf{\hat{y}}- c \left(z_{16} - \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (4a) | H X |
| $\mathbf{B_{64}}$ | = | $\left(x_{16} + \frac{1}{2}\right) \, \mathbf{a}_{1}- \left(y_{16} - \frac{1}{2}\right) \, \mathbf{a}_{2}- z_{16} \, \mathbf{a}_{3}$ | = | $a \left(x_{16} + \frac{1}{2}\right) \,\mathbf{\hat{x}}- b \left(y_{16} - \frac{1}{2}\right) \,\mathbf{\hat{y}}- c z_{16} \,\mathbf{\hat{z}}$ | (4a) | H X |
| $\mathbf{B_{65}}$ | = | $x_{17} \, \mathbf{a}_{1}+y_{17} \, \mathbf{a}_{2}+z_{17} \, \mathbf{a}_{3}$ | = | $a x_{17} \,\mathbf{\hat{x}}+b y_{17} \,\mathbf{\hat{y}}+c z_{17} \,\mathbf{\hat{z}}$ | (4a) | H XI |
| $\mathbf{B_{66}}$ | = | $- \left(x_{17} - \frac{1}{2}\right) \, \mathbf{a}_{1}- y_{17} \, \mathbf{a}_{2}+\left(z_{17} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- a \left(x_{17} - \frac{1}{2}\right) \,\mathbf{\hat{x}}- b y_{17} \,\mathbf{\hat{y}}+c \left(z_{17} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (4a) | H XI |
| $\mathbf{B_{67}}$ | = | $- x_{17} \, \mathbf{a}_{1}+\left(y_{17} + \frac{1}{2}\right) \, \mathbf{a}_{2}- \left(z_{17} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- a x_{17} \,\mathbf{\hat{x}}+b \left(y_{17} + \frac{1}{2}\right) \,\mathbf{\hat{y}}- c \left(z_{17} - \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (4a) | H XI |
| $\mathbf{B_{68}}$ | = | $\left(x_{17} + \frac{1}{2}\right) \, \mathbf{a}_{1}- \left(y_{17} - \frac{1}{2}\right) \, \mathbf{a}_{2}- z_{17} \, \mathbf{a}_{3}$ | = | $a \left(x_{17} + \frac{1}{2}\right) \,\mathbf{\hat{x}}- b \left(y_{17} - \frac{1}{2}\right) \,\mathbf{\hat{y}}- c z_{17} \,\mathbf{\hat{z}}$ | (4a) | H XI |
| $\mathbf{B_{69}}$ | = | $x_{18} \, \mathbf{a}_{1}+y_{18} \, \mathbf{a}_{2}+z_{18} \, \mathbf{a}_{3}$ | = | $a x_{18} \,\mathbf{\hat{x}}+b y_{18} \,\mathbf{\hat{y}}+c z_{18} \,\mathbf{\hat{z}}$ | (4a) | H XII |
| $\mathbf{B_{70}}$ | = | $- \left(x_{18} - \frac{1}{2}\right) \, \mathbf{a}_{1}- y_{18} \, \mathbf{a}_{2}+\left(z_{18} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- a \left(x_{18} - \frac{1}{2}\right) \,\mathbf{\hat{x}}- b y_{18} \,\mathbf{\hat{y}}+c \left(z_{18} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (4a) | H XII |
| $\mathbf{B_{71}}$ | = | $- x_{18} \, \mathbf{a}_{1}+\left(y_{18} + \frac{1}{2}\right) \, \mathbf{a}_{2}- \left(z_{18} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- a x_{18} \,\mathbf{\hat{x}}+b \left(y_{18} + \frac{1}{2}\right) \,\mathbf{\hat{y}}- c \left(z_{18} - \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (4a) | H XII |
| $\mathbf{B_{72}}$ | = | $\left(x_{18} + \frac{1}{2}\right) \, \mathbf{a}_{1}- \left(y_{18} - \frac{1}{2}\right) \, \mathbf{a}_{2}- z_{18} \, \mathbf{a}_{3}$ | = | $a \left(x_{18} + \frac{1}{2}\right) \,\mathbf{\hat{x}}- b \left(y_{18} - \frac{1}{2}\right) \,\mathbf{\hat{y}}- c z_{18} \,\mathbf{\hat{z}}$ | (4a) | H XII |
| $\mathbf{B_{73}}$ | = | $x_{19} \, \mathbf{a}_{1}+y_{19} \, \mathbf{a}_{2}+z_{19} \, \mathbf{a}_{3}$ | = | $a x_{19} \,\mathbf{\hat{x}}+b y_{19} \,\mathbf{\hat{y}}+c z_{19} \,\mathbf{\hat{z}}$ | (4a) | O I |
| $\mathbf{B_{74}}$ | = | $- \left(x_{19} - \frac{1}{2}\right) \, \mathbf{a}_{1}- y_{19} \, \mathbf{a}_{2}+\left(z_{19} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- a \left(x_{19} - \frac{1}{2}\right) \,\mathbf{\hat{x}}- b y_{19} \,\mathbf{\hat{y}}+c \left(z_{19} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (4a) | O I |
| $\mathbf{B_{75}}$ | = | $- x_{19} \, \mathbf{a}_{1}+\left(y_{19} + \frac{1}{2}\right) \, \mathbf{a}_{2}- \left(z_{19} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- a x_{19} \,\mathbf{\hat{x}}+b \left(y_{19} + \frac{1}{2}\right) \,\mathbf{\hat{y}}- c \left(z_{19} - \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (4a) | O I |
| $\mathbf{B_{76}}$ | = | $\left(x_{19} + \frac{1}{2}\right) \, \mathbf{a}_{1}- \left(y_{19} - \frac{1}{2}\right) \, \mathbf{a}_{2}- z_{19} \, \mathbf{a}_{3}$ | = | $a \left(x_{19} + \frac{1}{2}\right) \,\mathbf{\hat{x}}- b \left(y_{19} - \frac{1}{2}\right) \,\mathbf{\hat{y}}- c z_{19} \,\mathbf{\hat{z}}$ | (4a) | O I |
| $\mathbf{B_{77}}$ | = | $x_{20} \, \mathbf{a}_{1}+y_{20} \, \mathbf{a}_{2}+z_{20} \, \mathbf{a}_{3}$ | = | $a x_{20} \,\mathbf{\hat{x}}+b y_{20} \,\mathbf{\hat{y}}+c z_{20} \,\mathbf{\hat{z}}$ | (4a) | O II |
| $\mathbf{B_{78}}$ | = | $- \left(x_{20} - \frac{1}{2}\right) \, \mathbf{a}_{1}- y_{20} \, \mathbf{a}_{2}+\left(z_{20} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- a \left(x_{20} - \frac{1}{2}\right) \,\mathbf{\hat{x}}- b y_{20} \,\mathbf{\hat{y}}+c \left(z_{20} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (4a) | O II |
| $\mathbf{B_{79}}$ | = | $- x_{20} \, \mathbf{a}_{1}+\left(y_{20} + \frac{1}{2}\right) \, \mathbf{a}_{2}- \left(z_{20} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- a x_{20} \,\mathbf{\hat{x}}+b \left(y_{20} + \frac{1}{2}\right) \,\mathbf{\hat{y}}- c \left(z_{20} - \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (4a) | O II |
| $\mathbf{B_{80}}$ | = | $\left(x_{20} + \frac{1}{2}\right) \, \mathbf{a}_{1}- \left(y_{20} - \frac{1}{2}\right) \, \mathbf{a}_{2}- z_{20} \, \mathbf{a}_{3}$ | = | $a \left(x_{20} + \frac{1}{2}\right) \,\mathbf{\hat{x}}- b \left(y_{20} - \frac{1}{2}\right) \,\mathbf{\hat{y}}- c z_{20} \,\mathbf{\hat{z}}$ | (4a) | O II |
| $\mathbf{B_{81}}$ | = | $x_{21} \, \mathbf{a}_{1}+y_{21} \, \mathbf{a}_{2}+z_{21} \, \mathbf{a}_{3}$ | = | $a x_{21} \,\mathbf{\hat{x}}+b y_{21} \,\mathbf{\hat{y}}+c z_{21} \,\mathbf{\hat{z}}$ | (4a) | O III |
| $\mathbf{B_{82}}$ | = | $- \left(x_{21} - \frac{1}{2}\right) \, \mathbf{a}_{1}- y_{21} \, \mathbf{a}_{2}+\left(z_{21} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- a \left(x_{21} - \frac{1}{2}\right) \,\mathbf{\hat{x}}- b y_{21} \,\mathbf{\hat{y}}+c \left(z_{21} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (4a) | O III |
| $\mathbf{B_{83}}$ | = | $- x_{21} \, \mathbf{a}_{1}+\left(y_{21} + \frac{1}{2}\right) \, \mathbf{a}_{2}- \left(z_{21} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- a x_{21} \,\mathbf{\hat{x}}+b \left(y_{21} + \frac{1}{2}\right) \,\mathbf{\hat{y}}- c \left(z_{21} - \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (4a) | O III |
| $\mathbf{B_{84}}$ | = | $\left(x_{21} + \frac{1}{2}\right) \, \mathbf{a}_{1}- \left(y_{21} - \frac{1}{2}\right) \, \mathbf{a}_{2}- z_{21} \, \mathbf{a}_{3}$ | = | $a \left(x_{21} + \frac{1}{2}\right) \,\mathbf{\hat{x}}- b \left(y_{21} - \frac{1}{2}\right) \,\mathbf{\hat{y}}- c z_{21} \,\mathbf{\hat{z}}$ | (4a) | O III |
| $\mathbf{B_{85}}$ | = | $x_{22} \, \mathbf{a}_{1}+y_{22} \, \mathbf{a}_{2}+z_{22} \, \mathbf{a}_{3}$ | = | $a x_{22} \,\mathbf{\hat{x}}+b y_{22} \,\mathbf{\hat{y}}+c z_{22} \,\mathbf{\hat{z}}$ | (4a) | O IV |
| $\mathbf{B_{86}}$ | = | $- \left(x_{22} - \frac{1}{2}\right) \, \mathbf{a}_{1}- y_{22} \, \mathbf{a}_{2}+\left(z_{22} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- a \left(x_{22} - \frac{1}{2}\right) \,\mathbf{\hat{x}}- b y_{22} \,\mathbf{\hat{y}}+c \left(z_{22} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (4a) | O IV |
| $\mathbf{B_{87}}$ | = | $- x_{22} \, \mathbf{a}_{1}+\left(y_{22} + \frac{1}{2}\right) \, \mathbf{a}_{2}- \left(z_{22} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- a x_{22} \,\mathbf{\hat{x}}+b \left(y_{22} + \frac{1}{2}\right) \,\mathbf{\hat{y}}- c \left(z_{22} - \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (4a) | O IV |
| $\mathbf{B_{88}}$ | = | $\left(x_{22} + \frac{1}{2}\right) \, \mathbf{a}_{1}- \left(y_{22} - \frac{1}{2}\right) \, \mathbf{a}_{2}- z_{22} \, \mathbf{a}_{3}$ | = | $a \left(x_{22} + \frac{1}{2}\right) \,\mathbf{\hat{x}}- b \left(y_{22} - \frac{1}{2}\right) \,\mathbf{\hat{y}}- c z_{22} \,\mathbf{\hat{z}}$ | (4a) | O IV |
| $\mathbf{B_{89}}$ | = | $x_{23} \, \mathbf{a}_{1}+y_{23} \, \mathbf{a}_{2}+z_{23} \, \mathbf{a}_{3}$ | = | $a x_{23} \,\mathbf{\hat{x}}+b y_{23} \,\mathbf{\hat{y}}+c z_{23} \,\mathbf{\hat{z}}$ | (4a) | O V |
| $\mathbf{B_{90}}$ | = | $- \left(x_{23} - \frac{1}{2}\right) \, \mathbf{a}_{1}- y_{23} \, \mathbf{a}_{2}+\left(z_{23} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- a \left(x_{23} - \frac{1}{2}\right) \,\mathbf{\hat{x}}- b y_{23} \,\mathbf{\hat{y}}+c \left(z_{23} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (4a) | O V |
| $\mathbf{B_{91}}$ | = | $- x_{23} \, \mathbf{a}_{1}+\left(y_{23} + \frac{1}{2}\right) \, \mathbf{a}_{2}- \left(z_{23} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- a x_{23} \,\mathbf{\hat{x}}+b \left(y_{23} + \frac{1}{2}\right) \,\mathbf{\hat{y}}- c \left(z_{23} - \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (4a) | O V |
| $\mathbf{B_{92}}$ | = | $\left(x_{23} + \frac{1}{2}\right) \, \mathbf{a}_{1}- \left(y_{23} - \frac{1}{2}\right) \, \mathbf{a}_{2}- z_{23} \, \mathbf{a}_{3}$ | = | $a \left(x_{23} + \frac{1}{2}\right) \,\mathbf{\hat{x}}- b \left(y_{23} - \frac{1}{2}\right) \,\mathbf{\hat{y}}- c z_{23} \,\mathbf{\hat{z}}$ | (4a) | O V |
| $\mathbf{B_{93}}$ | = | $x_{24} \, \mathbf{a}_{1}+y_{24} \, \mathbf{a}_{2}+z_{24} \, \mathbf{a}_{3}$ | = | $a x_{24} \,\mathbf{\hat{x}}+b y_{24} \,\mathbf{\hat{y}}+c z_{24} \,\mathbf{\hat{z}}$ | (4a) | O VI |
| $\mathbf{B_{94}}$ | = | $- \left(x_{24} - \frac{1}{2}\right) \, \mathbf{a}_{1}- y_{24} \, \mathbf{a}_{2}+\left(z_{24} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- a \left(x_{24} - \frac{1}{2}\right) \,\mathbf{\hat{x}}- b y_{24} \,\mathbf{\hat{y}}+c \left(z_{24} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (4a) | O VI |
| $\mathbf{B_{95}}$ | = | $- x_{24} \, \mathbf{a}_{1}+\left(y_{24} + \frac{1}{2}\right) \, \mathbf{a}_{2}- \left(z_{24} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- a x_{24} \,\mathbf{\hat{x}}+b \left(y_{24} + \frac{1}{2}\right) \,\mathbf{\hat{y}}- c \left(z_{24} - \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (4a) | O VI |
| $\mathbf{B_{96}}$ | = | $\left(x_{24} + \frac{1}{2}\right) \, \mathbf{a}_{1}- \left(y_{24} - \frac{1}{2}\right) \, \mathbf{a}_{2}- z_{24} \, \mathbf{a}_{3}$ | = | $a \left(x_{24} + \frac{1}{2}\right) \,\mathbf{\hat{x}}- b \left(y_{24} - \frac{1}{2}\right) \,\mathbf{\hat{y}}- c z_{24} \,\mathbf{\hat{z}}$ | (4a) | O VI |
References
- G. M. Brown and H. A. Levy, α-D-Glucose: further refinement based on neutron-diffraction data, Acta Crystallogr. Sect. B 35, 656–659 (1979), doi:10.1107/S0567740879004374.
Found in
- T. Chihi, M. A. Ghebouli, and M. Fatmi, Predictive physical study of two different crystalline forms of glucose, Biochem. Biophys. Rep. 25, 100923 (2021), doi:10.1016/j.bbrep.2021.100923.
First cited in
- N. Anderson, M. J. Mehl, H. Eckert, S. Divilov, X. Campilongo, S. Curtarolo, The AFLOW Library of Crystallographic Prototypes: Part 5. Submitted to Computational Materials Science (2026).
Geometry files
Prototype Generator
aflow --proto=AB2C_oP96_19_6a_12a_6a --params=$a,b/a,c/a,x_{1},y_{1},z_{1},x_{2},y_{2},z_{2},x_{3},y_{3},z_{3},x_{4},y_{4},z_{4},x_{5},y_{5},z_{5},x_{6},y_{6},z_{6},x_{7},y_{7},z_{7},x_{8},y_{8},z_{8},x_{9},y_{9},z_{9},x_{10},y_{10},z_{10},x_{11},y_{11},z_{11},x_{12},y_{12},z_{12},x_{13},y_{13},z_{13},x_{14},y_{14},z_{14},x_{15},y_{15},z_{15},x_{16},y_{16},z_{16},x_{17},y_{17},z_{17},x_{18},y_{18},z_{18},x_{19},y_{19},z_{19},x_{20},y_{20},z_{20},x_{21},y_{21},z_{21},x_{22},y_{22},z_{22},x_{23},y_{23},z_{23},x_{24},y_{24},z_{24}$