Concept
Tetrahedral bipyramid
Concepts associés (4)
Icosahedral bipyramid
In 4-dimensional geometry, the icosahedral bipyramid is the direct sum of a icosahedron and a segment, {3,5} + { }. Each face of a central icosahedron is attached with two tetrahedra, creating 40 tetrahedral cells, 80 triangular faces, 54 edges, and 14 vertices. An icosahedral bipyramid can be seen as two icosahedral pyramids augmented together at their bases. It is the dual of a dodecahedral prism, Coxeter-Dynkin diagram , so the bipyramid can be described as . Both have Coxeter notation symmetry [2,3,5], order 240.
Dodecahedral bipyramid
In 4-dimensional geometry, the dodecahedral bipyramid is the direct sum of a dodecahedron and a segment, {5,3} + { }. Each face of a central dodecahedron is attached with two pentagonal pyramids, creating 24 pentagonal pyramidal cells, 72 isosceles triangular faces, 70 edges, and 22 vertices. A dodecahedral bipyramid can be seen as two dodecahedral pyramids augmented together at their base. It is the dual of a icosahedral prism.
Cubical bipyramid
In 4-dimensional geometry, the cubical bipyramid is the direct sum of a cube and a segment, {4,3} + { }. Each face of a central cube is attached with two square pyramids, creating 12 square pyramidal cells, 30 triangular faces, 28 edges, and 10 vertices. A cubical bipyramid can be seen as two cubic pyramids augmented together at their base. It is the dual of a octahedral prism. Being convex and regular-faced, it is a CRF polytope. It is a Hanner polytope with coordinates: [2] (0, 0, 0; ±1) [8] (±1, ±1, ±1;
Bipyramide
En géométrie, un diamant ou bipyramide, ou encore dipyramide, est un polyèdre constitué de deux pyramides symétriques dont la même base forme un polygone régulier. L'ordre du diamant est l'ordre du polygone de la base. C'est aussi l'ordre du sommet de chaque pyramide. Il existe un unique diamant dans les polyèdres réguliers: l'octaèdre. Cependant, pour chaque ordre d'un diamant, il existe un diamant dont toutes les faces sont des triangles isocèles isométriques.