Concept
Hécatonicosachore 5/2,3,5
Concepts associés (4)
Regular 4-polytope
In mathematics, a regular 4-polytope is a regular four-dimensional polytope. They are the four-dimensional analogues of the regular polyhedra in three dimensions and the regular polygons in two dimensions. There are six convex and ten star regular 4-polytopes, giving a total of sixteen. The convex regular 4-polytopes were first described by the Swiss mathematician Ludwig Schläfli in the mid-19th century. He discovered that there are precisely six such figures.
Pentagonal polytope
In geometry, a pentagonal polytope is a regular polytope in n dimensions constructed from the Hn Coxeter group. The family was named by H. S. M. Coxeter, because the two-dimensional pentagonal polytope is a pentagon. It can be named by its Schläfli symbol as {5, 3n − 2} (dodecahedral) or {3n − 2, 5} (icosahedral). The family starts as 1-polytopes and ends with n = 5 as infinite tessellations of 4-dimensional hyperbolic space. There are two types of pentagonal polytopes; they may be termed the dodecahedral and icosahedral types, by their three-dimensional members.
Hécatonicosachore 5/2,5,5/2
En géométrie, l'hécatonicosachore 5/2,5,5/2 est un 4-polytope régulier étoilé ayant pour symbole de Schläfli {5/2,5,5/2}. C'est l'un des 10 polychores de Schläfli-Hess. Il est l'un des deux polytopes à être son propre dual. Il a la même que le grand hexacosichore et l'hécatonicosachore icosaédral, ainsi que la même disposition de faces que l'hécatonicosachore 5/2,3,5.
Hécatonicosachore icosaédral
In geometry, the icosahedral 120-cell, polyicosahedron, faceted 600-cell or icosaplex is a regular star 4-polytope with Schläfli symbol {3,5,5/2}. It is one of 10 regular Schläfli-Hess polytopes. It is constructed by 5 icosahedra around each edge in a pentagrammic figure. The vertex figure is a great dodecahedron. It has the same edge arrangement as the 600-cell, grand 120-cell and great 120-cell, and shares its vertices with all other Schläfli–Hess 4-polytopes except the great grand stellated 120-cell (another stellation of the 120-cell).