In 5-dimensional geometry, there are 19 uniform polytopes with A5 symmetry. There is one self-dual regular form, the 5-simplex with 6 vertices. Each can...
subgroups. Symmetric orthographic projections of these 39 polytopes can be made in the E6, D5, D4, D2, A5, A4, A3 Coxeter planes. Ak has k+1 symmetry, Dk has...
In 8-dimensional geometry, the 421 is a semiregular uniform 8-polytope, constructed within the symmetry of the E8 group. It was discovered by Thorold Gosset...
Symmetric orthographic projections of these 255 polytopes can be made in the E8, E7, E6, D7, D6, D5, D4, D3, A7, A5 Coxeter planes. Ak has [k+1] symmetry, Dk...
In 8-dimensional geometry, the 142 is a uniform 8-polytope, constructed within the symmetry of the E8 group. Its Coxeter symbol is 142, describing its...
122 polytope is a uniform polytope, constructed from the E6 group. It was first published in E. L. Elte's 1912 listing of semiregular polytopes, named...
these 64 polytopes can be made in the B6, B5, B4, B3, B2, A5, A3, Coxeter planes. Ak has [k+1] symmetry, and Bk has [2k] symmetry. These 64 polytopes are each...
Symmetric orthographic projections of these 127 polytopes can be made in the E7, E6, D6, D5, D4, D3, A6, A5, A4, A3, A2 Coxeter planes. Ak has k+1 symmetry...
Symmetric orthographic projections of these 64 polytopes can be made in the D8, D7, D6, D5, D4, D3, A5, A3, Coxeter planes. Ak has [k+1] symmetry, Dk...
subgroups. Symmetric orthographic projections of these 16 polytopes can be made in the D6, D5, D4, D3, A5, A3, Coxeter planes. Ak has [k+1] symmetry, Dk has...
Symmetric orthographic projections of these 32 polytopes can be made in the D7, D6, D5, D4, D3, A5, A3, Coxeter planes. Ak has [k+1] symmetry, Dk has...
tetrahedron of the cube is an example of a Heronian tetrahedron. Every regular polytope, including the regular tetrahedron, has its characteristic orthoscheme...
projections of these 135 polytopes can be made in the A8, A7, A6, A5, A4, A3, A2 Coxeter planes. Ak has [k+1] symmetry. These 135 polytopes are each shown in...
subgroups. Symmetric orthographic projections of these 35 polytopes can be made in the A6, A5, A4, A3, A2 Coxeter planes. Ak graphs have [k+1] symmetry...
Symmetric orthographic projections of these 256 polytopes can be made in the B8, B7, B6, B5, B4, B3, B2, A7, A5, A3, Coxeter planes. Ak has [k+1] symmetry...
subgroups. Symmetric orthographic projections of these 71 polytopes can be made in the A7, A6, A5, A4, A3, A2 Coxeter planes. Ak has [k+1] symmetry. For...
In 7-dimensional geometry, 132 is a uniform polytope, constructed from the E7 group. Its Coxeter symbol is 132, describing its bifurcating Coxeter-Dynkin...
face, an edge of the face, a vertex of the edge, and the null polytope. An abstract polytope is said to be regular if its combinatorial symmetries are transitive...
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