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It is an example of a Platonic solid and of a deltahedron. The icosahedral graph represents the skeleton of a regular icosahedron. Many polyhedra are constructed from the regular icosahedron. For example, most of the Kepler–Poinsot polyhedron is constructed by faceting. Some of the Johnson solids can be constructed by removing the pentagonal ...
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 ...
For example, the icosahedron is {3,5+} 1,0, and pentakis dodecahedron, {3,5+} 1,1 is seen as a regular dodecahedron with pentagonal faces divided into 5 triangles. The primary face of the subdivision is called a principal polyhedral triangle (PPT) or the breakdown structure. Calculating a single PPT allows the entire figure to be created.
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.
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. The name comes from Ancient Greek εἴκοσι (eíkosi) 'twenty' and ἕδρα (hédra) 'seat'.
Simple examples of Goldberg polyhedra include the dodecahedron and truncated icosahedron. Other forms can be described by taking a chess knight move from one pentagon to the next: first take m steps in one direction, then turn 60° to the left and take n steps. Such a polyhedron is denoted GP(m,n).
An example is given by the regular icosahedron: if five of its triangles are removed, and are replaced by five congruent triangles forming an indentation into the polyhedron, the resulting surface metric stays unchanged. [7] This example uses the same creases for the convex and non-convex polyhedron, but that is not always the case.
It can be seen as the compound of an icosahedron and dodecahedron. It is one of four compounds constructed from a Platonic solid or Kepler-Poinsot solid, and its dual. It has icosahedral symmetry (I h) and the same vertex arrangement as a rhombic triacontahedron.