Truncated dodecahedron Truncated dodecahedron In geometry, the truncated dodecahedron is an Archimedean solid. It has 12 regular decagonal faces, 20 regular triangular faces, 60 vertices and 90 edges. This polyhedron can be formed from a dodecahedron by truncating (cutting off) the corners so the pentagon faces become decagons and the corners become triangles. It is used in the cell-transitive hyperbolic space-filling tessellation, the bitruncated icosahedral honeycomb. The area "A" and the volume "V" of a truncated dodecahedron of edge length "a" are: Cartesian coordinates for the vertices of a truncated dodecahedron with edge length 2"φ" − 2, centered at the origin, are
Pentakis dodecahedron buckminsterfullerene: each surface segment represents a carbon atom. Equivalently, a truncated icosahedron is a model of buckminsterfullerene, with each vertex representing a carbon atom. The "pentakis dodecahedron" is also a model of some icosahedrally symmetric viruses, such as Adeno-associated virus. These have 60 symmetry related capsid proteins, which combine to make the 60 symmetrical faces of a "pentakis dodecahedron". The pentakis dodecahedron has three symmetry positions, two on vertices, and one on a midedge: Pentakis dodecahedron In geometry, a pentakis dodecahedron or kisdodecahedron is a dodecahedron with a pentagonal pyramid covering each face; that is, it is the Kleetope of