Concept
Dual d'un polyèdre
Concepts associés (30)
Hypercubic honeycomb
In 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.
57-cell
In mathematics, the 57-cell (pentacontakaiheptachoron) is a self-dual abstract regular 4-polytope (four-dimensional polytope). Its 57 cells are hemi-dodecahedra. It also has 57 vertices, 171 edges and 171 two-dimensional faces. The symmetry order is 3420, from the product of the number of cells (57) and the symmetry of each cell (60). The symmetry abstract structure is the projective special linear group, L2(19). It has Schläfli type {5,3,5} with 5 hemi-dodecahedral cells around each edge. It was discovered by .
Polygone dual
En géométrie, les polygones peuvent être associés par paires de duaux, où les sommets de l'un correspondent aux côtés de l'autre. vignette|upright=1.5|La construction « de Dorman Luke » du dual d'un polyèdre, montrant une face rhombique duale à une face rectangulaire. Les polygones réguliers sont autoduaux, c'est-à-dire qu'ils sont leur propre polygone dual. Le dual d'un polygone isogonal est un polygone isotoxal. Par exemple, le rectangle (isogonal) et le losange (isotoxal) sont duaux.
Grand hécatonicosachore étoilé
vignette|243x243px| Projection orthogonale En géométrie, le grand hécatonicosachore étoilé, ou hécatonicosachore 5,5/2,5, est un 4-polytope régulier étoilé ayant pour symbole de Schläfli {5,5/2,5}. C'est l'un des 10 polychores de Schläfli-Hess. C'est l'un des deux polytopes qui est son propre dual. Il a la même que l'hexacosichore et l'hécatonicosachore icosaédral, ainsi que la même disposition de faces que l'hécatonicosachore 5,3,5/2.
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.
Pyramide pentagonale
En géométrie, la pyramide pentagonale est un des solides de Johnson (J2). Comme toute pyramide, c'est un polyèdre autodual. Il peut être vu comme le "couvercle" d'un icosaèdre; le reste de l'icosaèdre forme la pyramide pentagonale gyroallongée, J11. Les 92 solides de Johnson ont été nommés et décrits par Norman Johnson en 1966. Plus généralement, une pyramide pentagonale de sommet uniforme d'ordre 2 peut être définie avec une base pentagonale régulière et 5 côtés en forme de triangles isocèles de hauteur quelconque.
Pyramide carrée allongée
In geometry, the elongated square pyramid is one of the Johnson solids (J_8). As the name suggests, it can be constructed by elongating a square pyramid (J_1) by attaching a cube to its square base. Like any elongated pyramid, it is topologically (but not geometrically) self-dual. The following formulae for the height (), surface area () and volume () can be used if all faces are regular, with edge length : The dual of the elongated square pyramid has 9 faces: 4 triangular, 1 square and 4 trapezoidal.
Icosahedral honeycomb
In geometry, the icosahedral honeycomb is one of four compact, regular, space-filling tessellations (or honeycombs) in hyperbolic 3-space. With Schläfli symbol {3,5,3}, there are three icosahedra around each edge, and 12 icosahedra around each vertex, in a regular dodecahedral vertex figure. The dihedral angle of a regular icosahedron is around 138.2°, so it is impossible to fit three icosahedra around an edge in Euclidean 3-space. However, in hyperbolic space, properly scaled icosahedra can have dihedral angles of exactly 120 degrees, so three of those can fit around an edge.
Dihedron
A dihedron is a type of polyhedron, made of two polygon faces which share the same set of n edges. In three-dimensional Euclidean space, it is degenerate if its faces are flat, while in three-dimensional spherical space, a dihedron with flat faces can be thought of as a lens, an example of which is the fundamental domain of a lens space L(p,q). Dihedra have also been called bihedra, flat polyhedra, or doubly covered polygons.
Sphère inscrite
In geometry, the inscribed sphere or insphere of a convex polyhedron is a sphere that is contained within the polyhedron and tangent to each of the polyhedron's faces. It is the largest sphere that is contained wholly within the polyhedron, and is dual to the dual polyhedron's circumsphere. The radius of the sphere inscribed in a polyhedron P is called the inradius of P. All regular polyhedra have inscribed spheres, but most irregular polyhedra do not have all facets tangent to a common sphere, although it is still possible to define the largest contained sphere for such shapes.