Petit rhombicosidodécaèdrevignette|Patron. Le petit rhombicosidodécaèdre est un solide d'Archimède. Il possède 20 faces triangulaires régulières, 30 faces carrées régulières, 12 faces pentagonales régulières, 60 sommets et 120 arêtes. Le nom rhombicosidodécaèdre fait référence au fait que les 30 faces carrées sont placées dans les mêmes plans que les 30 faces du triacontaèdre rhombique qui est le dual de l'icosidodécaèdre. Il peut aussi être appelé un dodécaèdre étendu ou un icosaèdre étendu à partir des opérations de troncature du solide uniforme.
Icosidodécaèdre tronquéthumb|Patron (géométrie) L'icosidodécaèdre tronqué est un solide d'Archimède. Il possède 30 faces carrées régulières, 20 faces hexagonales régulières, 12 faces décagonales régulières, 120 sommets et 180 arêtes. Puisque chacune des faces possède un centre de symétrie, le grand rhombicosidodécaèdre est un zonoèdre (à quinze générateurs). Son dual est l'hexaki-icosaèdre, solide de Catalan. D'autres noms incluent : grand rhombicosidodécaèdre ; icosidodécaèdre rhombitronqué ; icosidodécaèdre .
Grand dodécaèdre tronquéIn geometry, the truncated great dodecahedron is a nonconvex uniform polyhedron, indexed as U37. It has 24 faces (12 pentagrams and 12 decagons), 90 edges, and 60 vertices. It is given a Schläfli symbol t{5,5/2}. It shares its vertex arrangement with three other uniform polyhedra: the nonconvex great rhombicosidodecahedron, the great dodecicosidodecahedron, and the great rhombidodecahedron; and with the uniform compounds of 6 or 12 pentagonal prisms.
Cube tronquéIn geometry, the truncated cube, or truncated hexahedron, is an Archimedean solid. It has 14 regular faces (6 octagonal and 8 triangular), 36 edges, and 24 vertices. If the truncated cube has unit edge length, its dual triakis octahedron has edges of lengths 2 and 2 + . The area A and the volume V of a truncated cube of edge length a are: The truncated cube has five special orthogonal projections, centered, on a vertex, on two types of edges, and two types of faces: triangles, and octagons.
DodécadodécaèdreIn geometry, the dodecadodecahedron is a nonconvex uniform polyhedron, indexed as U36. It is the rectification of the great dodecahedron (and that of its dual, the small stellated dodecahedron). It was discovered independently by , and . The edges of this model form 10 central hexagons, and these, projected onto a sphere, become 10 great circles. These 10, along with the great circles from projections of two other polyhedra, form the 31 great circles of the spherical icosahedron used in construction of geodesic domes.
Grand icosidodécaèdreIn geometry, the great icosidodecahedron is a nonconvex uniform polyhedron, indexed as U54. It has 32 faces (20 triangles and 12 pentagrams), 60 edges, and 30 vertices. It is given a Schläfli symbol r{3,}. It is the rectification of the great stellated dodecahedron and the great icosahedron. It was discovered independently by , and . The figure is a rectification of the great icosahedron or the great stellated dodecahedron, much as the (small) icosidodecahedron is related to the (small) icosahedron and (small) dodecahedron, and the cuboctahedron to the cube and octahedron.
Petit cubicuboctaèdreIn geometry, the small cubicuboctahedron is a uniform star polyhedron, indexed as U13. It has 20 faces (8 triangles, 6 squares, and 6 octagons), 48 edges, and 24 vertices. Its vertex figure is a crossed quadrilateral. The small cubicuboctahedron is a faceting of the rhombicuboctahedron. Its square faces and its octagonal faces are parallel to those of a cube, while its triangular faces are parallel to those of an octahedron: hence the name cubicuboctahedron.
Petit dodécicosaèdreIn geometry, the small dodecicosahedron (or small dodekicosahedron) is a nonconvex uniform polyhedron, indexed as U50. It has 32 faces (20 hexagons and 12 decagons), 120 edges, and 60 vertices. Its vertex figure is a crossed quadrilateral. It shares its vertex arrangement with the great stellated truncated dodecahedron. It additionally shares its edges with the small icosicosidodecahedron (having the hexagonal faces in common) and the small ditrigonal dodecicosidodecahedron (having the decagonal faces in common).
Grand dodécaèdre étoilé tronquéIn geometry, the great stellated truncated dodecahedron (or quasitruncated great stellated dodecahedron or great stellatruncated dodecahedron) is a nonconvex uniform polyhedron, indexed as U66. It has 32 faces (20 triangles and 12 decagrams), 90 edges, and 60 vertices. It is given a Schläfli symbol t0,1{5/3,3}.
Grand dodécicosidodécaèdreIn geometry, the great dodecicosidodecahedron (or great dodekicosidodecahedron) is a nonconvex uniform polyhedron, indexed as U61. It has 44 faces (20 triangles, 12 pentagrams and 12 decagrams), 120 edges and 60 vertices. It shares its vertex arrangement with the truncated great dodecahedron and the uniform compounds of 6 or 12 pentagonal prisms. It additionally shares its edge arrangement with the nonconvex great rhombicosidodecahedron (having the triangular and pentagrammic faces in common), and with the great rhombidodecahedron (having the decagrammic faces in common).
