FCC C$_{60}$ Buckminsterfullerene Structure: A_cF240_202_h2i-001
| Prototype | C |
| AFLOW prototype label | A_cF240_202_h2i-001 |
| Mineral name | buckminsterfullerene |
| ICSD | 74523 |
| Pearson symbol | cF240 |
| Space group number | 202 |
| Space group symbol | $Fm\overline{3}$ |
| AFLOW prototype command |
aflow --proto=A_cF240_202_h2i-001
--params=$a, \allowbreak y_{1}, \allowbreak z_{1}, \allowbreak x_{2}, \allowbreak y_{2}, \allowbreak z_{2}, \allowbreak x_{3}, \allowbreak y_{3}, \allowbreak z_{3}$ |
- This is an approximate representation of the structure of C$_{60}$ buckminsterfullerene. As noted by the authors,
a careful analysis of the intensity data reveals that the molecules must pack in an uncorrelated array, in full agreement with the results from most previous diffraction and spectroscopic determinations.
- The C$_{60}$ molecules are centered on the sites of an fcc lattice.
- Below 249K there is a transition to a simple cubic phase of C$_{60}$.
\[ \begin{array}{ccc}
\mathbf{a_{1}}&=&\frac{1}{2}a \,\mathbf{\hat{y}}+\frac{1}{2}a \,\mathbf{\hat{z}}\\\mathbf{a_{2}}&=&\frac{1}{2}a \,\mathbf{\hat{x}}+\frac{1}{2}a \,\mathbf{\hat{z}}\\\mathbf{a_{3}}&=&\frac{1}{2}a \,\mathbf{\hat{x}}+\frac{1}{2}a \,\mathbf{\hat{y}}
\end{array}\]
Basis vectors
| Lattice coordinates | Cartesian coordinates | Wyckoff position | Atom type | |||
|---|---|---|---|---|---|---|
| $\mathbf{B_{1}}$ | = | $\left(y_{1} + z_{1}\right) \, \mathbf{a}_{1}- \left(y_{1} - z_{1}\right) \, \mathbf{a}_{2}+\left(y_{1} - z_{1}\right) \, \mathbf{a}_{3}$ | = | $a y_{1} \,\mathbf{\hat{y}}+a z_{1} \,\mathbf{\hat{z}}$ | (48h) | C I |
| $\mathbf{B_{2}}$ | = | $- \left(y_{1} - z_{1}\right) \, \mathbf{a}_{1}+\left(y_{1} + z_{1}\right) \, \mathbf{a}_{2}- \left(y_{1} + z_{1}\right) \, \mathbf{a}_{3}$ | = | $- a y_{1} \,\mathbf{\hat{y}}+a z_{1} \,\mathbf{\hat{z}}$ | (48h) | C I |
| $\mathbf{B_{3}}$ | = | $\left(y_{1} - z_{1}\right) \, \mathbf{a}_{1}- \left(y_{1} + z_{1}\right) \, \mathbf{a}_{2}+\left(y_{1} + z_{1}\right) \, \mathbf{a}_{3}$ | = | $a y_{1} \,\mathbf{\hat{y}}- a z_{1} \,\mathbf{\hat{z}}$ | (48h) | C I |
| $\mathbf{B_{4}}$ | = | $- \left(y_{1} + z_{1}\right) \, \mathbf{a}_{1}+\left(y_{1} - z_{1}\right) \, \mathbf{a}_{2}- \left(y_{1} - z_{1}\right) \, \mathbf{a}_{3}$ | = | $- a y_{1} \,\mathbf{\hat{y}}- a z_{1} \,\mathbf{\hat{z}}$ | (48h) | C I |
| $\mathbf{B_{5}}$ | = | $\left(y_{1} - z_{1}\right) \, \mathbf{a}_{1}+\left(y_{1} + z_{1}\right) \, \mathbf{a}_{2}- \left(y_{1} - z_{1}\right) \, \mathbf{a}_{3}$ | = | $a z_{1} \,\mathbf{\hat{x}}+a y_{1} \,\mathbf{\hat{z}}$ | (48h) | C I |
| $\mathbf{B_{6}}$ | = | $- \left(y_{1} + z_{1}\right) \, \mathbf{a}_{1}- \left(y_{1} - z_{1}\right) \, \mathbf{a}_{2}+\left(y_{1} + z_{1}\right) \, \mathbf{a}_{3}$ | = | $a z_{1} \,\mathbf{\hat{x}}- a y_{1} \,\mathbf{\hat{z}}$ | (48h) | C I |
| $\mathbf{B_{7}}$ | = | $\left(y_{1} + z_{1}\right) \, \mathbf{a}_{1}+\left(y_{1} - z_{1}\right) \, \mathbf{a}_{2}- \left(y_{1} + z_{1}\right) \, \mathbf{a}_{3}$ | = | $- a z_{1} \,\mathbf{\hat{x}}+a y_{1} \,\mathbf{\hat{z}}$ | (48h) | C I |
| $\mathbf{B_{8}}$ | = | $- \left(y_{1} - z_{1}\right) \, \mathbf{a}_{1}- \left(y_{1} + z_{1}\right) \, \mathbf{a}_{2}+\left(y_{1} - z_{1}\right) \, \mathbf{a}_{3}$ | = | $- a z_{1} \,\mathbf{\hat{x}}- a y_{1} \,\mathbf{\hat{z}}$ | (48h) | C I |
| $\mathbf{B_{9}}$ | = | $- \left(y_{1} - z_{1}\right) \, \mathbf{a}_{1}+\left(y_{1} - z_{1}\right) \, \mathbf{a}_{2}+\left(y_{1} + z_{1}\right) \, \mathbf{a}_{3}$ | = | $a y_{1} \,\mathbf{\hat{x}}+a z_{1} \,\mathbf{\hat{y}}$ | (48h) | C I |
| $\mathbf{B_{10}}$ | = | $\left(y_{1} + z_{1}\right) \, \mathbf{a}_{1}- \left(y_{1} + z_{1}\right) \, \mathbf{a}_{2}- \left(y_{1} - z_{1}\right) \, \mathbf{a}_{3}$ | = | $- a y_{1} \,\mathbf{\hat{x}}+a z_{1} \,\mathbf{\hat{y}}$ | (48h) | C I |
| $\mathbf{B_{11}}$ | = | $- \left(y_{1} + z_{1}\right) \, \mathbf{a}_{1}+\left(y_{1} + z_{1}\right) \, \mathbf{a}_{2}+\left(y_{1} - z_{1}\right) \, \mathbf{a}_{3}$ | = | $a y_{1} \,\mathbf{\hat{x}}- a z_{1} \,\mathbf{\hat{y}}$ | (48h) | C I |
| $\mathbf{B_{12}}$ | = | $\left(y_{1} - z_{1}\right) \, \mathbf{a}_{1}- \left(y_{1} - z_{1}\right) \, \mathbf{a}_{2}- \left(y_{1} + z_{1}\right) \, \mathbf{a}_{3}$ | = | $- a y_{1} \,\mathbf{\hat{x}}- a z_{1} \,\mathbf{\hat{y}}$ | (48h) | C I |
| $\mathbf{B_{13}}$ | = | $\left(- x_{2} + y_{2} + z_{2}\right) \, \mathbf{a}_{1}+\left(x_{2} - y_{2} + z_{2}\right) \, \mathbf{a}_{2}+\left(x_{2} + y_{2} - z_{2}\right) \, \mathbf{a}_{3}$ | = | $a x_{2} \,\mathbf{\hat{x}}+a y_{2} \,\mathbf{\hat{y}}+a z_{2} \,\mathbf{\hat{z}}$ | (96i) | C II |
| $\mathbf{B_{14}}$ | = | $\left(x_{2} - y_{2} + z_{2}\right) \, \mathbf{a}_{1}+\left(- x_{2} + y_{2} + z_{2}\right) \, \mathbf{a}_{2}- \left(x_{2} + y_{2} + z_{2}\right) \, \mathbf{a}_{3}$ | = | $- a x_{2} \,\mathbf{\hat{x}}- a y_{2} \,\mathbf{\hat{y}}+a z_{2} \,\mathbf{\hat{z}}$ | (96i) | C II |
| $\mathbf{B_{15}}$ | = | $\left(x_{2} + y_{2} - z_{2}\right) \, \mathbf{a}_{1}- \left(x_{2} + y_{2} + z_{2}\right) \, \mathbf{a}_{2}+\left(- x_{2} + y_{2} + z_{2}\right) \, \mathbf{a}_{3}$ | = | $- a x_{2} \,\mathbf{\hat{x}}+a y_{2} \,\mathbf{\hat{y}}- a z_{2} \,\mathbf{\hat{z}}$ | (96i) | C II |
| $\mathbf{B_{16}}$ | = | $- \left(x_{2} + y_{2} + z_{2}\right) \, \mathbf{a}_{1}+\left(x_{2} + y_{2} - z_{2}\right) \, \mathbf{a}_{2}+\left(x_{2} - y_{2} + z_{2}\right) \, \mathbf{a}_{3}$ | = | $a x_{2} \,\mathbf{\hat{x}}- a y_{2} \,\mathbf{\hat{y}}- a z_{2} \,\mathbf{\hat{z}}$ | (96i) | C II |
| $\mathbf{B_{17}}$ | = | $\left(x_{2} + y_{2} - z_{2}\right) \, \mathbf{a}_{1}+\left(- x_{2} + y_{2} + z_{2}\right) \, \mathbf{a}_{2}+\left(x_{2} - y_{2} + z_{2}\right) \, \mathbf{a}_{3}$ | = | $a z_{2} \,\mathbf{\hat{x}}+a x_{2} \,\mathbf{\hat{y}}+a y_{2} \,\mathbf{\hat{z}}$ | (96i) | C II |
| $\mathbf{B_{18}}$ | = | $- \left(x_{2} + y_{2} + z_{2}\right) \, \mathbf{a}_{1}+\left(x_{2} - y_{2} + z_{2}\right) \, \mathbf{a}_{2}+\left(- x_{2} + y_{2} + z_{2}\right) \, \mathbf{a}_{3}$ | = | $a z_{2} \,\mathbf{\hat{x}}- a x_{2} \,\mathbf{\hat{y}}- a y_{2} \,\mathbf{\hat{z}}$ | (96i) | C II |
| $\mathbf{B_{19}}$ | = | $\left(- x_{2} + y_{2} + z_{2}\right) \, \mathbf{a}_{1}+\left(x_{2} + y_{2} - z_{2}\right) \, \mathbf{a}_{2}- \left(x_{2} + y_{2} + z_{2}\right) \, \mathbf{a}_{3}$ | = | $- a z_{2} \,\mathbf{\hat{x}}- a x_{2} \,\mathbf{\hat{y}}+a y_{2} \,\mathbf{\hat{z}}$ | (96i) | C II |
| $\mathbf{B_{20}}$ | = | $\left(x_{2} - y_{2} + z_{2}\right) \, \mathbf{a}_{1}- \left(x_{2} + y_{2} + z_{2}\right) \, \mathbf{a}_{2}+\left(x_{2} + y_{2} - z_{2}\right) \, \mathbf{a}_{3}$ | = | $- a z_{2} \,\mathbf{\hat{x}}+a x_{2} \,\mathbf{\hat{y}}- a y_{2} \,\mathbf{\hat{z}}$ | (96i) | C II |
| $\mathbf{B_{21}}$ | = | $\left(x_{2} - y_{2} + z_{2}\right) \, \mathbf{a}_{1}+\left(x_{2} + y_{2} - z_{2}\right) \, \mathbf{a}_{2}+\left(- x_{2} + y_{2} + z_{2}\right) \, \mathbf{a}_{3}$ | = | $a y_{2} \,\mathbf{\hat{x}}+a z_{2} \,\mathbf{\hat{y}}+a x_{2} \,\mathbf{\hat{z}}$ | (96i) | C II |
| $\mathbf{B_{22}}$ | = | $\left(- x_{2} + y_{2} + z_{2}\right) \, \mathbf{a}_{1}- \left(x_{2} + y_{2} + z_{2}\right) \, \mathbf{a}_{2}+\left(x_{2} - y_{2} + z_{2}\right) \, \mathbf{a}_{3}$ | = | $- a y_{2} \,\mathbf{\hat{x}}+a z_{2} \,\mathbf{\hat{y}}- a x_{2} \,\mathbf{\hat{z}}$ | (96i) | C II |
| $\mathbf{B_{23}}$ | = | $- \left(x_{2} + y_{2} + z_{2}\right) \, \mathbf{a}_{1}+\left(- x_{2} + y_{2} + z_{2}\right) \, \mathbf{a}_{2}+\left(x_{2} + y_{2} - z_{2}\right) \, \mathbf{a}_{3}$ | = | $a y_{2} \,\mathbf{\hat{x}}- a z_{2} \,\mathbf{\hat{y}}- a x_{2} \,\mathbf{\hat{z}}$ | (96i) | C II |
| $\mathbf{B_{24}}$ | = | $\left(x_{2} + y_{2} - z_{2}\right) \, \mathbf{a}_{1}+\left(x_{2} - y_{2} + z_{2}\right) \, \mathbf{a}_{2}- \left(x_{2} + y_{2} + z_{2}\right) \, \mathbf{a}_{3}$ | = | $- a y_{2} \,\mathbf{\hat{x}}- a z_{2} \,\mathbf{\hat{y}}+a x_{2} \,\mathbf{\hat{z}}$ | (96i) | C II |
| $\mathbf{B_{25}}$ | = | $\left(x_{2} - y_{2} - z_{2}\right) \, \mathbf{a}_{1}- \left(x_{2} - y_{2} + z_{2}\right) \, \mathbf{a}_{2}- \left(x_{2} + y_{2} - z_{2}\right) \, \mathbf{a}_{3}$ | = | $- a x_{2} \,\mathbf{\hat{x}}- a y_{2} \,\mathbf{\hat{y}}- a z_{2} \,\mathbf{\hat{z}}$ | (96i) | C II |
| $\mathbf{B_{26}}$ | = | $- \left(x_{2} - y_{2} + z_{2}\right) \, \mathbf{a}_{1}+\left(x_{2} - y_{2} - z_{2}\right) \, \mathbf{a}_{2}+\left(x_{2} + y_{2} + z_{2}\right) \, \mathbf{a}_{3}$ | = | $a x_{2} \,\mathbf{\hat{x}}+a y_{2} \,\mathbf{\hat{y}}- a z_{2} \,\mathbf{\hat{z}}$ | (96i) | C II |
| $\mathbf{B_{27}}$ | = | $- \left(x_{2} + y_{2} - z_{2}\right) \, \mathbf{a}_{1}+\left(x_{2} + y_{2} + z_{2}\right) \, \mathbf{a}_{2}+\left(x_{2} - y_{2} - z_{2}\right) \, \mathbf{a}_{3}$ | = | $a x_{2} \,\mathbf{\hat{x}}- a y_{2} \,\mathbf{\hat{y}}+a z_{2} \,\mathbf{\hat{z}}$ | (96i) | C II |
| $\mathbf{B_{28}}$ | = | $\left(x_{2} + y_{2} + z_{2}\right) \, \mathbf{a}_{1}- \left(x_{2} + y_{2} - z_{2}\right) \, \mathbf{a}_{2}- \left(x_{2} - y_{2} + z_{2}\right) \, \mathbf{a}_{3}$ | = | $- a x_{2} \,\mathbf{\hat{x}}+a y_{2} \,\mathbf{\hat{y}}+a z_{2} \,\mathbf{\hat{z}}$ | (96i) | C II |
| $\mathbf{B_{29}}$ | = | $- \left(x_{2} + y_{2} - z_{2}\right) \, \mathbf{a}_{1}+\left(x_{2} - y_{2} - z_{2}\right) \, \mathbf{a}_{2}- \left(x_{2} - y_{2} + z_{2}\right) \, \mathbf{a}_{3}$ | = | $- a z_{2} \,\mathbf{\hat{x}}- a x_{2} \,\mathbf{\hat{y}}- a y_{2} \,\mathbf{\hat{z}}$ | (96i) | C II |
| $\mathbf{B_{30}}$ | = | $\left(x_{2} + y_{2} + z_{2}\right) \, \mathbf{a}_{1}- \left(x_{2} - y_{2} + z_{2}\right) \, \mathbf{a}_{2}+\left(x_{2} - y_{2} - z_{2}\right) \, \mathbf{a}_{3}$ | = | $- a z_{2} \,\mathbf{\hat{x}}+a x_{2} \,\mathbf{\hat{y}}+a y_{2} \,\mathbf{\hat{z}}$ | (96i) | C II |
| $\mathbf{B_{31}}$ | = | $\left(x_{2} - y_{2} - z_{2}\right) \, \mathbf{a}_{1}- \left(x_{2} + y_{2} - z_{2}\right) \, \mathbf{a}_{2}+\left(x_{2} + y_{2} + z_{2}\right) \, \mathbf{a}_{3}$ | = | $a z_{2} \,\mathbf{\hat{x}}+a x_{2} \,\mathbf{\hat{y}}- a y_{2} \,\mathbf{\hat{z}}$ | (96i) | C II |
| $\mathbf{B_{32}}$ | = | $- \left(x_{2} - y_{2} + z_{2}\right) \, \mathbf{a}_{1}+\left(x_{2} + y_{2} + z_{2}\right) \, \mathbf{a}_{2}- \left(x_{2} + y_{2} - z_{2}\right) \, \mathbf{a}_{3}$ | = | $a z_{2} \,\mathbf{\hat{x}}- a x_{2} \,\mathbf{\hat{y}}+a y_{2} \,\mathbf{\hat{z}}$ | (96i) | C II |
| $\mathbf{B_{33}}$ | = | $- \left(x_{2} - y_{2} + z_{2}\right) \, \mathbf{a}_{1}- \left(x_{2} + y_{2} - z_{2}\right) \, \mathbf{a}_{2}+\left(x_{2} - y_{2} - z_{2}\right) \, \mathbf{a}_{3}$ | = | $- a y_{2} \,\mathbf{\hat{x}}- a z_{2} \,\mathbf{\hat{y}}- a x_{2} \,\mathbf{\hat{z}}$ | (96i) | C II |
| $\mathbf{B_{34}}$ | = | $\left(x_{2} - y_{2} - z_{2}\right) \, \mathbf{a}_{1}+\left(x_{2} + y_{2} + z_{2}\right) \, \mathbf{a}_{2}- \left(x_{2} - y_{2} + z_{2}\right) \, \mathbf{a}_{3}$ | = | $a y_{2} \,\mathbf{\hat{x}}- a z_{2} \,\mathbf{\hat{y}}+a x_{2} \,\mathbf{\hat{z}}$ | (96i) | C II |
| $\mathbf{B_{35}}$ | = | $\left(x_{2} + y_{2} + z_{2}\right) \, \mathbf{a}_{1}+\left(x_{2} - y_{2} - z_{2}\right) \, \mathbf{a}_{2}- \left(x_{2} + y_{2} - z_{2}\right) \, \mathbf{a}_{3}$ | = | $- a y_{2} \,\mathbf{\hat{x}}+a z_{2} \,\mathbf{\hat{y}}+a x_{2} \,\mathbf{\hat{z}}$ | (96i) | C II |
| $\mathbf{B_{36}}$ | = | $- \left(x_{2} + y_{2} - z_{2}\right) \, \mathbf{a}_{1}- \left(x_{2} - y_{2} + z_{2}\right) \, \mathbf{a}_{2}+\left(x_{2} + y_{2} + z_{2}\right) \, \mathbf{a}_{3}$ | = | $a y_{2} \,\mathbf{\hat{x}}+a z_{2} \,\mathbf{\hat{y}}- a x_{2} \,\mathbf{\hat{z}}$ | (96i) | C II |
| $\mathbf{B_{37}}$ | = | $\left(- x_{3} + y_{3} + z_{3}\right) \, \mathbf{a}_{1}+\left(x_{3} - y_{3} + z_{3}\right) \, \mathbf{a}_{2}+\left(x_{3} + y_{3} - z_{3}\right) \, \mathbf{a}_{3}$ | = | $a x_{3} \,\mathbf{\hat{x}}+a y_{3} \,\mathbf{\hat{y}}+a z_{3} \,\mathbf{\hat{z}}$ | (96i) | C III |
| $\mathbf{B_{38}}$ | = | $\left(x_{3} - y_{3} + z_{3}\right) \, \mathbf{a}_{1}+\left(- x_{3} + y_{3} + z_{3}\right) \, \mathbf{a}_{2}- \left(x_{3} + y_{3} + z_{3}\right) \, \mathbf{a}_{3}$ | = | $- a x_{3} \,\mathbf{\hat{x}}- a y_{3} \,\mathbf{\hat{y}}+a z_{3} \,\mathbf{\hat{z}}$ | (96i) | C III |
| $\mathbf{B_{39}}$ | = | $\left(x_{3} + y_{3} - z_{3}\right) \, \mathbf{a}_{1}- \left(x_{3} + y_{3} + z_{3}\right) \, \mathbf{a}_{2}+\left(- x_{3} + y_{3} + z_{3}\right) \, \mathbf{a}_{3}$ | = | $- a x_{3} \,\mathbf{\hat{x}}+a y_{3} \,\mathbf{\hat{y}}- a z_{3} \,\mathbf{\hat{z}}$ | (96i) | C III |
| $\mathbf{B_{40}}$ | = | $- \left(x_{3} + y_{3} + z_{3}\right) \, \mathbf{a}_{1}+\left(x_{3} + y_{3} - z_{3}\right) \, \mathbf{a}_{2}+\left(x_{3} - y_{3} + z_{3}\right) \, \mathbf{a}_{3}$ | = | $a x_{3} \,\mathbf{\hat{x}}- a y_{3} \,\mathbf{\hat{y}}- a z_{3} \,\mathbf{\hat{z}}$ | (96i) | C III |
| $\mathbf{B_{41}}$ | = | $\left(x_{3} + y_{3} - z_{3}\right) \, \mathbf{a}_{1}+\left(- x_{3} + y_{3} + z_{3}\right) \, \mathbf{a}_{2}+\left(x_{3} - y_{3} + z_{3}\right) \, \mathbf{a}_{3}$ | = | $a z_{3} \,\mathbf{\hat{x}}+a x_{3} \,\mathbf{\hat{y}}+a y_{3} \,\mathbf{\hat{z}}$ | (96i) | C III |
| $\mathbf{B_{42}}$ | = | $- \left(x_{3} + y_{3} + z_{3}\right) \, \mathbf{a}_{1}+\left(x_{3} - y_{3} + z_{3}\right) \, \mathbf{a}_{2}+\left(- x_{3} + y_{3} + z_{3}\right) \, \mathbf{a}_{3}$ | = | $a z_{3} \,\mathbf{\hat{x}}- a x_{3} \,\mathbf{\hat{y}}- a y_{3} \,\mathbf{\hat{z}}$ | (96i) | C III |
| $\mathbf{B_{43}}$ | = | $\left(- x_{3} + y_{3} + z_{3}\right) \, \mathbf{a}_{1}+\left(x_{3} + y_{3} - z_{3}\right) \, \mathbf{a}_{2}- \left(x_{3} + y_{3} + z_{3}\right) \, \mathbf{a}_{3}$ | = | $- a z_{3} \,\mathbf{\hat{x}}- a x_{3} \,\mathbf{\hat{y}}+a y_{3} \,\mathbf{\hat{z}}$ | (96i) | C III |
| $\mathbf{B_{44}}$ | = | $\left(x_{3} - y_{3} + z_{3}\right) \, \mathbf{a}_{1}- \left(x_{3} + y_{3} + z_{3}\right) \, \mathbf{a}_{2}+\left(x_{3} + y_{3} - z_{3}\right) \, \mathbf{a}_{3}$ | = | $- a z_{3} \,\mathbf{\hat{x}}+a x_{3} \,\mathbf{\hat{y}}- a y_{3} \,\mathbf{\hat{z}}$ | (96i) | C III |
| $\mathbf{B_{45}}$ | = | $\left(x_{3} - y_{3} + z_{3}\right) \, \mathbf{a}_{1}+\left(x_{3} + y_{3} - z_{3}\right) \, \mathbf{a}_{2}+\left(- x_{3} + y_{3} + z_{3}\right) \, \mathbf{a}_{3}$ | = | $a y_{3} \,\mathbf{\hat{x}}+a z_{3} \,\mathbf{\hat{y}}+a x_{3} \,\mathbf{\hat{z}}$ | (96i) | C III |
| $\mathbf{B_{46}}$ | = | $\left(- x_{3} + y_{3} + z_{3}\right) \, \mathbf{a}_{1}- \left(x_{3} + y_{3} + z_{3}\right) \, \mathbf{a}_{2}+\left(x_{3} - y_{3} + z_{3}\right) \, \mathbf{a}_{3}$ | = | $- a y_{3} \,\mathbf{\hat{x}}+a z_{3} \,\mathbf{\hat{y}}- a x_{3} \,\mathbf{\hat{z}}$ | (96i) | C III |
| $\mathbf{B_{47}}$ | = | $- \left(x_{3} + y_{3} + z_{3}\right) \, \mathbf{a}_{1}+\left(- x_{3} + y_{3} + z_{3}\right) \, \mathbf{a}_{2}+\left(x_{3} + y_{3} - z_{3}\right) \, \mathbf{a}_{3}$ | = | $a y_{3} \,\mathbf{\hat{x}}- a z_{3} \,\mathbf{\hat{y}}- a x_{3} \,\mathbf{\hat{z}}$ | (96i) | C III |
| $\mathbf{B_{48}}$ | = | $\left(x_{3} + y_{3} - z_{3}\right) \, \mathbf{a}_{1}+\left(x_{3} - y_{3} + z_{3}\right) \, \mathbf{a}_{2}- \left(x_{3} + y_{3} + z_{3}\right) \, \mathbf{a}_{3}$ | = | $- a y_{3} \,\mathbf{\hat{x}}- a z_{3} \,\mathbf{\hat{y}}+a x_{3} \,\mathbf{\hat{z}}$ | (96i) | C III |
| $\mathbf{B_{49}}$ | = | $\left(x_{3} - y_{3} - z_{3}\right) \, \mathbf{a}_{1}- \left(x_{3} - y_{3} + z_{3}\right) \, \mathbf{a}_{2}- \left(x_{3} + y_{3} - z_{3}\right) \, \mathbf{a}_{3}$ | = | $- a x_{3} \,\mathbf{\hat{x}}- a y_{3} \,\mathbf{\hat{y}}- a z_{3} \,\mathbf{\hat{z}}$ | (96i) | C III |
| $\mathbf{B_{50}}$ | = | $- \left(x_{3} - y_{3} + z_{3}\right) \, \mathbf{a}_{1}+\left(x_{3} - y_{3} - z_{3}\right) \, \mathbf{a}_{2}+\left(x_{3} + y_{3} + z_{3}\right) \, \mathbf{a}_{3}$ | = | $a x_{3} \,\mathbf{\hat{x}}+a y_{3} \,\mathbf{\hat{y}}- a z_{3} \,\mathbf{\hat{z}}$ | (96i) | C III |
| $\mathbf{B_{51}}$ | = | $- \left(x_{3} + y_{3} - z_{3}\right) \, \mathbf{a}_{1}+\left(x_{3} + y_{3} + z_{3}\right) \, \mathbf{a}_{2}+\left(x_{3} - y_{3} - z_{3}\right) \, \mathbf{a}_{3}$ | = | $a x_{3} \,\mathbf{\hat{x}}- a y_{3} \,\mathbf{\hat{y}}+a z_{3} \,\mathbf{\hat{z}}$ | (96i) | C III |
| $\mathbf{B_{52}}$ | = | $\left(x_{3} + y_{3} + z_{3}\right) \, \mathbf{a}_{1}- \left(x_{3} + y_{3} - z_{3}\right) \, \mathbf{a}_{2}- \left(x_{3} - y_{3} + z_{3}\right) \, \mathbf{a}_{3}$ | = | $- a x_{3} \,\mathbf{\hat{x}}+a y_{3} \,\mathbf{\hat{y}}+a z_{3} \,\mathbf{\hat{z}}$ | (96i) | C III |
| $\mathbf{B_{53}}$ | = | $- \left(x_{3} + y_{3} - z_{3}\right) \, \mathbf{a}_{1}+\left(x_{3} - y_{3} - z_{3}\right) \, \mathbf{a}_{2}- \left(x_{3} - y_{3} + z_{3}\right) \, \mathbf{a}_{3}$ | = | $- a z_{3} \,\mathbf{\hat{x}}- a x_{3} \,\mathbf{\hat{y}}- a y_{3} \,\mathbf{\hat{z}}$ | (96i) | C III |
| $\mathbf{B_{54}}$ | = | $\left(x_{3} + y_{3} + z_{3}\right) \, \mathbf{a}_{1}- \left(x_{3} - y_{3} + z_{3}\right) \, \mathbf{a}_{2}+\left(x_{3} - y_{3} - z_{3}\right) \, \mathbf{a}_{3}$ | = | $- a z_{3} \,\mathbf{\hat{x}}+a x_{3} \,\mathbf{\hat{y}}+a y_{3} \,\mathbf{\hat{z}}$ | (96i) | C III |
| $\mathbf{B_{55}}$ | = | $\left(x_{3} - y_{3} - z_{3}\right) \, \mathbf{a}_{1}- \left(x_{3} + y_{3} - z_{3}\right) \, \mathbf{a}_{2}+\left(x_{3} + y_{3} + z_{3}\right) \, \mathbf{a}_{3}$ | = | $a z_{3} \,\mathbf{\hat{x}}+a x_{3} \,\mathbf{\hat{y}}- a y_{3} \,\mathbf{\hat{z}}$ | (96i) | C III |
| $\mathbf{B_{56}}$ | = | $- \left(x_{3} - y_{3} + z_{3}\right) \, \mathbf{a}_{1}+\left(x_{3} + y_{3} + z_{3}\right) \, \mathbf{a}_{2}- \left(x_{3} + y_{3} - z_{3}\right) \, \mathbf{a}_{3}$ | = | $a z_{3} \,\mathbf{\hat{x}}- a x_{3} \,\mathbf{\hat{y}}+a y_{3} \,\mathbf{\hat{z}}$ | (96i) | C III |
| $\mathbf{B_{57}}$ | = | $- \left(x_{3} - y_{3} + z_{3}\right) \, \mathbf{a}_{1}- \left(x_{3} + y_{3} - z_{3}\right) \, \mathbf{a}_{2}+\left(x_{3} - y_{3} - z_{3}\right) \, \mathbf{a}_{3}$ | = | $- a y_{3} \,\mathbf{\hat{x}}- a z_{3} \,\mathbf{\hat{y}}- a x_{3} \,\mathbf{\hat{z}}$ | (96i) | C III |
| $\mathbf{B_{58}}$ | = | $\left(x_{3} - y_{3} - z_{3}\right) \, \mathbf{a}_{1}+\left(x_{3} + y_{3} + z_{3}\right) \, \mathbf{a}_{2}- \left(x_{3} - y_{3} + z_{3}\right) \, \mathbf{a}_{3}$ | = | $a y_{3} \,\mathbf{\hat{x}}- a z_{3} \,\mathbf{\hat{y}}+a x_{3} \,\mathbf{\hat{z}}$ | (96i) | C III |
| $\mathbf{B_{59}}$ | = | $\left(x_{3} + y_{3} + z_{3}\right) \, \mathbf{a}_{1}+\left(x_{3} - y_{3} - z_{3}\right) \, \mathbf{a}_{2}- \left(x_{3} + y_{3} - z_{3}\right) \, \mathbf{a}_{3}$ | = | $- a y_{3} \,\mathbf{\hat{x}}+a z_{3} \,\mathbf{\hat{y}}+a x_{3} \,\mathbf{\hat{z}}$ | (96i) | C III |
| $\mathbf{B_{60}}$ | = | $- \left(x_{3} + y_{3} - z_{3}\right) \, \mathbf{a}_{1}- \left(x_{3} - y_{3} + z_{3}\right) \, \mathbf{a}_{2}+\left(x_{3} + y_{3} + z_{3}\right) \, \mathbf{a}_{3}$ | = | $a y_{3} \,\mathbf{\hat{x}}+a z_{3} \,\mathbf{\hat{y}}- a x_{3} \,\mathbf{\hat{z}}$ | (96i) | C III |
References
- D. L. Dorset and M. P. McCourt, Disorder and the molecular packing of C$_{60}$ buckminsterfullerene: a direct electron-crystallographic analysis, Acta Crystallogr. Sect. A 50, 344–351 (1994), doi:10.1107/S0108767393012607.
Prototype Generator
aflow --proto=A_cF240_202_h2i --params=$a,y_{1},z_{1},x_{2},y_{2},z_{2},x_{3},y_{3},z_{3}$