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In 4-dimensional geometry, there are 7 uniform 4-polytopes with reflections of D4 symmetry, all are shared with higher symmetry constructions in the B4...

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...

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...

convex 4-polytope (four-dimensional analogue of a Platonic solid) with Schläfli symbol {3,3,4}. It is one of the six regular convex 4-polytopes first described...

In geometry, a uniform 4-polytope (or uniform polychoron) is a 4-dimensional polytope which is vertex-transitive and whose cells are uniform polyhedra...

n-polytope elements are doubled from the (n − 1)-polytope elements and then creating new elements from the next lower element. Take an n-polytope with...

labels it the γ4 polytope. The term hypercube without a dimension reference is frequently treated as a synonym for this specific polytope. The Oxford English...

regular polytopes in Euclidean, spherical and hyperbolic spaces. This table shows a summary of regular polytope counts by rank. Only counting polytopes of...

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...

subgroups. 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...

In geometry, a polytope (e.g. a polygon or polyhedron) or a tiling is isogonal or vertex-transitive if all its vertices are equivalent under the symmetries...

deleting alternating vertices of the 5-cube, creates another uniform 5-polytope, called a 5-demicube, which is also part of an infinite family called the...

subgroups. 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...

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...

Its vertex figure is a 24-cell. The vertex arrangement is called the B4, D4, or F4 lattice. Hexadecachoric tetracomb/honeycomb Demitesseractic tetracomb/honeycomb...

hexagon). The square is in two families of polytopes in two dimensions: hypercube and the cross-polytope. The Schläfli symbol for the square is {4}....

In 6-dimensional geometry, the 221 polytope is a uniform 6-polytope, constructed within the symmetry of the E6 group. It was discovered by Thorold Gosset...

subgroups. Symmetric orthographic projections of these 8 polytopes can be made in the D5, D4, D3, A3, Coxeter planes. Ak has [k+1] symmetry, Dk has [2(k-1)]...

subgroups. 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...