Chamfered dodecahedron
Template:Short description Template:Infobox polyhedron
In geometry, the chamfered dodecahedron is a convex polyhedron with 80 vertices, 120 edges, and 42 faces: 30 hexagons and 12 pentagons. It is constructed as a chamfer (edge-truncation) of a regular dodecahedron. The pentagons are reduced in size and new hexagonal faces are added in place of all the original edges. Its dual is the pentakis icosidodecahedron.
It is also called a truncated rhombic triacontahedron, constructed as a truncation of the rhombic triacontahedron. It can more accurately be called an order-5 truncated rhombic triacontahedron because only the order-5 vertices are truncated. File:Chamfered dodecahedron.stl
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 DTemplate:Sub symmetry. The angles at the two vertices with vertex configuration Template:Math are and at the remaining four vertices with Template:Math, they are Template:Math each.
It is the Goldberg polyhedron Template:Math, containing pentagonal and hexagonal faces.Template:R
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 Template:Math. Occasionally, this shape is denoted Template:Math, describing its icosahedral symmetry and distinguishing it from other less-symmetric 80-vertex fullerenes.Template:R It is one of only four fullerenes found by Template:Harvtxt to have a skeleton that can be isometrically embeddable into an [[Taxicab geometry|LTemplate:Sub space]].[1]
Template:Truncated icosahedron vs chamfered dodecahedron
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
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