Search results
Results from the WOW.Com Content Network
Order-5 5-cell honeycomb; 120-cell honeycomb; Order-5 tesseractic honeycomb; Order-4 120-cell honeycomb; Order-5 120-cell honeycomb; Order-4 24-cell honeycomb; Cubic honeycomb honeycomb; Small stellated 120-cell honeycomb; Pentagrammic-order 600-cell honeycomb; Order-5 icosahedral 120-cell honeycomb; Great 120-cell honeycomb
[W] Wenninger, 1974, has 119 figures: 1–5 for the Platonic solids, 6–18 for the Archimedean solids, 19–66 for stellated forms including the 4 regular nonconvex polyhedra, and ended with 67–119 for the nonconvex uniform polyhedra.
Vertex the (n−5)-face of the 5-polytope; Edge the (n−4)-face of the 5-polytope; Face the peak or (n−3)-face of the 5-polytope; Cell the ridge or (n−2)-face of the 5-polytope; Hypercell or Teron the facet or (n−1)-face of the 5-polytope
{3,4} Defect 120° {3,5} Defect 60° {3,6} Defect 0° {4,3} Defect 90° {4,4} Defect 0° {5,3} Defect 36° {6,3} Defect 0° A vertex needs at least 3 faces, and an angle defect. A 0° angle defect will fill the Euclidean plane with a regular tiling. By Descartes' theorem, the number of vertices is 720°/defect.
Alternatively, if you expand each of five cubes by moving the faces away from the origin the right amount and rotating each of the five 72° around so they are equidistant from each other, without changing the orientation or size of the faces, and patch the pentagonal and triangular holes in the result, you get a rhombicosidodecahedron ...
4-faces 5-faces 6-faces 7-faces 8-faces χ 9-simplex {3 8} 10: 45: 120: 210: 252: 210: ... {4,3,6} Order-4 square tiling honeycomb ... As the last number in the ...
3 constructions for a {3,5+} 6,0; An icosahedron and related symmetry polyhedra can be used to define a high geodesic polyhedron by dividing triangular faces into smaller triangles, and projecting all the new vertices onto a sphere. Higher order polygonal faces can be divided into triangles by adding new vertices centered on each face.
There is a third topological polyhedral figure with 5 faces, degenerate as a polyhedron: it exists as a spherical tiling of digon faces, called a pentagonal hosohedron with Schläfli symbol {2,5}. It has 2 ( antipodal point ) vertices, 5 edges, and 5 digonal faces.