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In geometry, an icositetrahedron [1] is a polyhedron with 24 faces. There are many symmetric forms, and the ones with highest symmetry have chiral icosahedral symmetry: Four Catalan solids, convex: Triakis octahedron - isosceles triangles; Tetrakis hexahedron - isosceles triangles; Deltoidal icositetrahedron - kites; Pentagonal icositetrahedron ...
The deltoidal icositetrahedron (dual of the small rhombicuboctahedron) is tightly related to the disdyakis dodecahedron (dual of the great rhombicuboctahedron). The main difference is that the latter also has edges between the vertices on 3- and 4-fold symmetry axes (between yellow and red vertices in the images below) .
A geometric construction of the Tribonacci constant (AC), with compass and marked ruler, according to the method described by Xerardo Neira. 3d model of a pentagonal icositetrahedron. In geometry, a pentagonal icositetrahedron or pentagonal icosikaitetrahedron [1] is a Catalan solid which is the dual of the snub cube.
In geometry, the great deltoidal icositetrahedron (or great sagittal disdodecahedron) is the dual of the nonconvex great rhombicuboctahedron. Its faces are darts. Its faces are darts. Part of each dart lies inside the solid, hence is invisible in solid models.
In geometry, the small hexacronic icositetrahedron is the dual of the small cubicuboctahedron. It is visually identical to the small rhombihexacron . A part of each dart lies inside the solid, hence is invisible in solid models.
deltoidal icositetrahedron: 24 kites: 48 26 138.118° O h: disdyakis dodecahedron: 48 scalene triangles: 72 26 155.082° O h: pentagonal icositetrahedron: 24 pentagons: 60 38 136.309° O rhombic triacontahedron: 30 rhombi: 60 32 144° I h: triakis icosahedron: 60 isosceles triangles 90 32 160.613° I h: pentakis dodecahedron: 60 isosceles ...
For example, in a polyhedron (3-dimensional polytope), a face is a facet, an edge is a ridge, and a vertex is a peak. Vertex figure : not itself an element of a polytope, but a diagram showing how the elements meet.
An example can be found in the model of a buckminsterfullerene, a truncated icosahedron-shaped geodesic dome allotrope of elemental carbon discovered in 1985. [17] In other engineering and science applications, its shape was also the configuration of the lenses used for focusing the explosive shock waves of the detonators in both the gadget and ...
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