54-Faced Space-Filling Polyhedron
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Parts of a rhombic triacontahedron are removed to form a 54-faced spaceâfilling polyhedron. The locations of the removed parts correspond to the vertices of a cube inscribed in the rhombic triacontahedron. Each of the 8 removed parts is equivalent to half of an oblate golden rhombohedron. The faces include 6 golden rhombi and 8x6 triangles. When packed, each spaceâfilling polyhedron has 6+8 neighbors in the direction of faces and vertices of the cube, respectively. The centers of the polyhedra form a bodyâcentered cubic lattice.
Contributed by: Sándor Kabai (September 2007)
Open content licensed under CC BY-NC-SA
The illustration shows only 5 of the 14 connecting polyhedra around a central polyhedron.
"54-Faced Space-Filling Polyhedron"
Wolfram Demonstrations Project
Published: September 28 2007