Dodécadodécaèdre icositronquéIn geometry, the icositruncated dodecadodecahedron or icosidodecatruncated icosidodecahedron is a nonconvex uniform polyhedron, indexed as U45. Its convex hull is a nonuniform truncated icosidodecahedron. Cartesian coordinates for the vertices of an icositruncated dodecadodecahedron are all the even permutations of (±(2−1/τ), ±1, ±(2+τ)) (±1, ±1/τ2, ±(3τ−1)) (±2, ±2/τ, ±2τ) (±3, ±1/τ2, ±τ2) (±τ2, ±1, ±(3τ−2)) where τ = (1+)/2 is the golden ratio (sometimes written φ).
Prisme pentagrammiqueEn géométrie, le prisme pentagrammique est un élément de l'ensemble infini des prismes non-convexes formés par des côtés carrés et deux polygones étoilés réguliers, dans ce cas, deux pentagrammes. Ce polyèdre uniforme est indexé sous le nom U. C'est un cas particulier d'un prisme droit avec une base pentagrammique, qui en général, a des faces de côté rectangulaires. NOTE : Les faces pentagrammiques ont un intérieur ambigu parce qu'il s'auto-coupe.
Octagrammic antiprismIn geometry, the octagrammic antiprism is one in an infinite set of nonconvex antiprisms formed by triangle sides and two regular star polygon caps, in this case two octagrams.
Octagrammic crossed-antiprismIn geometry, the octagrammic crossed-antiprism is one in an infinite set of nonconvex antiprisms formed by triangle sides and two regular star polygon caps, in this case two octagrams.
Projective polyhedronIn geometry, a (globally) projective polyhedron is a tessellation of the real projective plane. These are projective analogs of spherical polyhedra – tessellations of the sphere – and toroidal polyhedra – tessellations of the toroids. Projective polyhedra are also referred to as elliptic tessellations or elliptic tilings, referring to the projective plane as (projective) elliptic geometry, by analogy with spherical tiling, a synonym for "spherical polyhedron".
Hypercubic honeycombIn geometry, a hypercubic honeycomb is a family of regular honeycombs (tessellations) in n-dimensional spaces with the Schläfli symbols {4,3...3,4} and containing the symmetry of Coxeter group R_n (or B^~_n–1) for n ≥ 3. The tessellation is constructed from 4 n-hypercubes per ridge. The vertex figure is a cross-polytope {3...3,4}. The hypercubic honeycombs are self-dual. Coxeter named this family as δ_n+1 for an n-dimensional honeycomb. A Wythoff construction is a method for constructing a uniform polyhedron or plane tiling.
Grand dodécaèdreEn géométrie, le grand dodécaèdre est un solide de Kepler-Poinsot. C'est un des quatre polyèdres réguliers non convexes. Il est composé de 12 faces pentagonales, avec cinq pentagones se rencontrant à chaque sommet, se coupant les uns les autres en créant un trajet pentagrammique. Les 12 sommets et les 30 arêtes sont partagées avec l'icosaèdre. Cette forme a été à la base du puzzle de type Rubik's Cube nommé l'étoile d'Alexandre. En enlevant les parties concaves, nous obtenons un icosaèdre.
Order-2 apeirogonal tilingIn geometry, an order-2 apeirogonal tiling, apeirogonal dihedron, or infinite dihedron is a tiling of the plane consisting of two apeirogons. It may be considered an improper regular tiling of the Euclidean plane, with Schläfli symbol {∞, 2}. Two apeirogons, joined along all their edges, can completely fill the entire plane as an apeirogon is infinite in size and has an interior angle of 180°, which is half of a full 360°. The apeirogonal tiling is the arithmetic limit of the family of dihedra {p, 2}, as p tends to infinity, thereby turning the dihedron into a Euclidean tiling.
