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Convex regular icosahedron A tensegrity icosahedron. In geometry, an icosahedron (/ ˌ aɪ k ɒ s ə ˈ h iː d r ən,-k ə-,-k oʊ-/ or / aɪ ˌ k ɒ s ə ˈ h iː d r ən / [1]) is a polyhedron with 20 faces.
In chemistry, the closo-carboranes are compounds with a shape resembling the regular icosahedron. [28] The crystal twinning with icosahedral shapes also occurs in crystals, especially nanoparticles. [29] Many borides and allotropes of boron such as α-and β-rhombohedral contain boron B 12 icosahedron as a basic structure unit. [30]
Icosahedral symmetry fundamental domains A soccer ball, a common example of a spherical truncated icosahedron, has full icosahedral symmetry. Rotations and reflections form the symmetry group of a great icosahedron. In mathematics, and especially in geometry, an object has icosahedral symmetry if it has the same symmetries as a regular icosahedron.
The graph is known as truncated icosahedral graph, and it has 60 vertices and 90 edges. It is an Archimedean graph because it resembles one of the Archimedean solids. It is a cubic graph , meaning that each vertex is incident to exactly three edges.
The capsids of some viruses have the shape of geodesic polyhedra, [1] [2] and some pollen grains are based on geodesic polyhedra. [3] Fullerene molecules have the shape of Goldberg polyhedra . Geodesic polyhedra are available as geometric primitives in the Blender 3D modeling software package , which calls them icospheres : they are an ...
There are five fundamental symmetry classes which have triangular fundamental domains: dihedral, cyclic, tetrahedral, octahedral, and icosahedral symmetry. This article lists the groups by Schoenflies notation, Coxeter notation, [1] orbifold notation, [2] and order.
Icosahedral 120-cell, Small stellated 120-cell, ... Table of Shapes Section Sub-Section Sup-Section Name Algebraic Curves ¿ Curves ¿ Curves: Cubic Plane Curve:
[K] Kaleido, 1993: The 80 figures were grouped by symmetry: 1–5 as representatives of the infinite families of prismatic forms with dihedral symmetry, 6–9 with tetrahedral symmetry, 10–26 with octahedral symmetry, 27–80 with icosahedral symmetry.