edge-contracted icosahedron is a polyhedron with 18 triangular faces, 27 edges, and 11 vertices. It can be constructed from the regular icosahedron,...

There is no 18-faced strictly convex deltahedron. However, the edge-contracted icosahedron gives an example of an octadecahedron that can either be made...

structure with C2v symmetry, the edge-contracted icosahedron, formed from a regular icosahedron with one edge contracted. It is the shape of the closo-boranate...

triangular cupola Triangulated truncated triangular bipyramid Edge-contracted icosahedron Hexagonal prism Hexagonal antiprism, Gyroelongated hexagonal...

the tetrahedron as a space-filling honeycomb. Orthobifastigium Edge-contracted icosahedron Elongated dodecahedron Elongated gyrobifastigium Convex Triamond...

into edges Example: P4O6 Electron count 4 × P + 6 × O = 4 × 5 + 6 × 6 = 56 It is a 5n + 6 structure with n = 10. Six vertices are inserted into edges As...

Jessen's icosahedron, sometimes called Jessen's orthogonal icosahedron, is a non-convex polyhedron with the same numbers of vertices, edges, and faces...

faces, 720 edges, and 120 vertices. It is the 4-dimensional analogue of the icosahedron, since it has five tetrahedra meeting at every edge, just as the...

Jessen's icosahedron's short edges stretch and its long edges are rigid, and in the rigid-edge transformation its long edges compress and its short edges are...

the poles. For N = 12, electrons reside at the vertices of a regular icosahedron. Geometric solutions of the Thomson problem for N = 4, 6, and 12 electrons...

tensegrity icosahedron, first studied by Snelson in 1949, has struts and tendons along the edges of a polyhedron called Jessen's icosahedron. It is a stable...

2007.[citation needed] A black-and-white patterned spherical truncated icosahedron design, brought to prominence by the Adidas Telstar, has become a symbol...

symmetry with the 120 basic disequilibrium LCD triangles of the spherical icosahedron. (See Sec. 1043.00.) The A and B Quanta Modules. Omnirationality: the...

eight golden rhombic faces with parallel edges. Removing only one zone of ten faces produces the rhombic icosahedron. Removing three zones of ten, eight,...

=V-E+F} where V, E, and F are respectively the numbers of vertices (corners), edges and faces in the given polyhedron. Any convex polyhedron's surface has Euler...

convex Platonic solids include the fivefold-symmetric dodecahedron and icosahedron, and there are also four star Kepler-Poinsot polyhedra with fivefold...

final of the 2005–06 season, the Finale used the traditional truncated icosahedron panel design for their balls. From then on the panels are the same as...

plane in such a way that its edges intersect only at their endpoints. In other words, it can be drawn in such a way that no edges cross each other. Such a...

or simple edge-unfolding? Is there a non-convex polyhedron without self-intersections with more than seven faces, all of which share an edge with each...

although the name also applies to other triakis shapes like the triakis icosahedron and triakis octahedron. It is the dual tessellation of the truncated...

Adidas for the 1970 FIFA World Cup. The first ball to use a truncated icosahedron design, with 12 black and 20 white patches intentionally used to improve...

that a sphere is smooth, while a cone or a pyramid, due to their vertex or edges, are not. The notion of a "regular surface" is a formalization of the notion...

tetrahedra (vertex figures), cubes (face prisms), and triangular prisms (edge figure prisms). The same process applied to a 16-cell also yields the same...

a factor-critical graph by contracting sufficiently many of its edges. The minimal sets of edges that need to be contracted to make a given graph G factor-critical...

is made from twenty stainless steel equilateral triangles (a regular icosahedron) and was designed and made by Brother Patrick, of Prinknash Abbey in...