Chamfered dodecahedron

Structure

These 12 order-5 vertices can be truncated such that all edges are of equal length. The original 30 rhombic faces become non-regular hexagons, and the truncated vertices become regular pentagons.

The hexagon faces can be equilateral but not regular with D symmetry. The angles at the two vertices with vertex configuration 6.6.6 are \arccos\left(\frac{-1}{\sqrt{5}}\right) \approx 116.565^{\circ} and at the remaining four vertices with 5.6.6, they are ≈121.717° each.

It is the Goldberg polyhedron G(2,0), containing pentagonal and hexagonal faces.

It also represents the exterior envelope of a cell-centered orthogonal projection of the 120-cell, one of six convex regular 4-polytopes.

Chemistry

The chamfered dodecahedron is the shape of the fullerene C. Occasionally, this shape is denoted C(I), describing its icosahedral symmetry and distinguishing it from other less-symmetric 80-vertex fullerenes. It is one of only four fullerenes found by to have a skeleton that can be isometrically embeddable into an L space.{{cite journal

Related polyhedra

This polyhedron looks very similar to the uniform truncated icosahedron, which has 12 pentagons, but only 20 hexagons. Image:Truncated rhombic triacontahedron.png|Truncated rhombic triacontahedronG(2,0) Image:Truncated icosahedron.png|Truncated icosahedronG(1,1) File:Ortho solid 120-cell.png|cell-centered orthogonal projection of the 120-cell

Related polytopes

It represents the exterior envelope of a cell-centered orthogonal projection of the 120-cell, one of six convex regular 4-polytopes, into 3 dimensions.

References

Bibliography

References

1. "C80 Isomers".