Elongated dodecahedronIn geometry, the elongated dodecahedron, extended rhombic dodecahedron, rhombo-hexagonal dodecahedron or hexarhombic dodecahedron is a convex dodecahedron with 8 rhombic and 4 hexagonal faces. The hexagons can be made equilateral, or regular depending on the shape of the rhombi. It can be seen as constructed from a rhombic dodecahedron elongated by a square prism. Along with the rhombic dodecahedron, it is a space-filling polyhedron, one of the five types of parallelohedron identified by Evgraf Fedorov that tile space face-to-face by translations.
Trapezo-rhombic dodecahedronIn geometry, the trapezo-rhombic dodecahedron or rhombo-trapezoidal dodecahedron is a convex dodecahedron with 6 rhombic and 6 trapezoidal faces. It has D_3h symmetry. A concave form can be constructed with an identical net, seen as excavating trigonal trapezohedra from the top and bottom. It is also called the trapezoidal dodecahedron. This polyhedron could be constructed by taking a tall uniform hexagonal prism, and making 3 angled cuts on the top and bottom.
First stellation of the rhombic dodecahedronIn geometry, the first stellation of the rhombic dodecahedron is a self-intersecting polyhedron with 12 faces, each of which is a non-convex hexagon. It is a stellation of the rhombic dodecahedron and has the same outer shell and the same visual appearance as two other shapes: a solid, Escher's solid, with 48 triangular faces, and a polyhedral compound of three flattened octahedra with 24 overlapping triangular faces. Escher's solid can tessellate space to form the stellated rhombic dodecahedral honeycomb.
PentakidodécaèdreUn pentakidodécaèdre est un polyèdre dual d'un solide d'Archimède, ou un solide de Catalan. Son dual est l'icosaèdre tronqué. Il peut être vu comme un dodécaèdre avec une pyramide pentagonale couvrant chaque face. Cette interprétation est exprimée dans le nom. 200pxLe pentakidodécaèdre dans un modèle de fullerène : chaque segment de surface représente un atome de carbone. Le Spaceship Earth à l'Epcot de Walt Disney World Resort est basé sur cette forme.
HexakioctaèdreUn hexakioctaèdre est un solide de Catalan et le dual d'un solide d'Archimède, le grand rhombicuboctaèdre. Comme tel, il est de faces uniformes mais avec des faces polygonales irrégulières. Il ressemble un peu à un dodécaèdre rhombique gonflé : si on remplace chaque face d'un dodécaèdre rhombique avec un sommet unique et quatre triangles d'une manière régulière, on a pour résultat un hexakioctaèdre. L'hexaki icosaèdre Robert Williams, The Geometrical Foundation of Natural Structure: A Source Book of Design, 1979, Disdyakis Dodecahedron - MathWorld.
Hexacontaèdre trapézoïdalEn géométrie, l'hexacontaèdre trapézoïdal, qualifié aussi de deltoïdal ou strombique, est un polyèdre dont les 60 faces sont des cerfs-volants convexes. Solide de Catalan, il est le dual du petit rhombicosidodécaèdre. Comme cinq autres solides de Catalan, il n'y a pas de cycle hamiltonien passant par tous ses sommets. Il est topologiquement équivalent à l'intersection de 6 cylindres de mêmes diamètres, chacun des axes passant par deux sommets opposés d'un icosaèdre régulier.
Order-4 pentagonal tilingIn geometry, the order-4 pentagonal tiling is a regular tiling of the hyperbolic plane. It has Schläfli symbol of {5,4}. It can also be called a pentapentagonal tiling in a bicolored quasiregular form. This tiling represents a hyperbolic kaleidoscope of 5 mirrors meeting as edges of a regular pentagon. This symmetry by orbifold notation is called 22222 with 5 order-2 mirror intersections. In Coxeter notation can be represented as [5,4], removing two of three mirrors (passing through the pentagon center) in the [5,4] symmetry.
