mathematics, a regular 4-polytope or regular polychoron is a regular four-dimensional polytope. They are the four-dimensional analogues of the regular polyhedra...

In geometry, a 4-polytope (sometimes also called a polychoron, polycell, or polyhedroid) is a four-dimensional polytope. It is a connected and closed figure...

In mathematics, a regular polytope is a polytope whose symmetry group acts transitively on its flags, thus giving it the highest degree of symmetry. In...

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

In elementary geometry, a polytope is a geometric object with flat sides (faces). Polytopes are the generalization of three-dimensional polyhedra to any...

In 4-dimensions, there are a large number of regular compounds of regular polytopes. Coxeter lists a few of these in his book Regular Polytopes. McMullen...

cells are uniform polyhedra, and faces are regular polygons. There are 47 non-prismatic convex uniform 4-polytopes. There are two infinite sets of convex...

2-dimensional cross-polytope is a square, a 3-dimensional cross-polytope is a regular octahedron, and a 4-dimensional cross-polytope is a 16-cell. Its facets...

the regular 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...

the six regular convex 4-polytopes (the four-dimensional analogues of the Platonic solids). A regular 5-cell can be constructed from a regular tetrahedron...

geometry, a five-dimensional polytope (or 5-polytope or polyteron) is a polytope in five-dimensional space, bounded by (4-polytope) facets, pairs of which...

convex regular 4-polytopes. The tesseract is also called an 8-cell, C8, (regular) octachoron, or cubic prism. It is the four-dimensional measure polytope, taken...

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...

six-dimensional geometry, a six-dimensional polytope or 6-polytope is a polytope, bounded by 5-polytope facets. A 6-polytope is a closed six-dimensional figure...

around each vertex and is represented by {4,3}. A regular 4-dimensional polytope, with r {p,q} regular polyhedral cells around each edge is represented...

In four-dimensional geometry, the 24-cell is the convex regular 4-polytope (four-dimensional analogue of a Platonic solid) with Schläfli symbol {3,4,3}...

the polytope. In two dimensions (and for two-dimensional faces of higher-dimensional polytopes) a stronger definition is used: only the regular polygons...

tiling[citation needed] convex regular 4-polytope 5-cell, the 4-space Simplex 8-cell, the 4-space Hypercube 16-cell, the 4-space Cross-polytope 24-cell 120-cell 600-cell...

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...

five tetrahedra is related to the regular 5-cell, the 4-simplex regular 4-polytope, which is also composed of 5 regular tetrahedra. In the 5-cell the tetrahedra...

generated from regular polyhedral and tilings. Each Convex regular 4-polytope has a rectified form as a uniform 4-polytope. A regular 4-polytope {p,q,r} has...

600-cell) is a convex uniform 4-polytope, being a runcination (a 3rd order truncation) of the regular 120-cell. There are 4 degrees of runcinations of the...

comparison mensuration. It also has many relations with other polytopes. The appearance of regular icosahedron can be found in nature, such as the virus with...

In geometry, a Petrie polygon for a regular polytope of n dimensions is a skew polygon in which every n – 1 consecutive sides (but no n) belongs to one...

operation on regular polytopes. The original edges are lost completely and the original faces remain as smaller copies of themselves. Bitruncated regular polytopes...

called the Boerdijk–Coxeter helix. In four dimensions, all the convex regular 4-polytopes with tetrahedral cells (the 5-cell, 16-cell and 600-cell) can be...

n-polytope and an m-polytope is an (n+m)-polytope, where n and m are dimensions of 2 (polygon) or higher. The lowest-dimensional duoprisms exist in 4-dimensional...

mathematics, an abstract polytope is an algebraic partially ordered set which captures the dyadic property of a traditional polytope without specifying purely...

broadly speaking, is the figure exposed when a corner of a polyhedron or polytope is sliced off. Take some corner or vertex of a polyhedron. Mark a point...

(pentacontakaiheptachoron) is a self-dual abstract regular 4-polytope (four-dimensional polytope). Its 57 cells are hemi-dodecahedra. It also has 57...