In geometry, an icosahedron (/ˌaɪkɒsəˈhiːdrən,-kə-,-koʊ-/ or /aɪˌkɒsəˈhiːdrən/[1]) is a polyhedron with 20 faces. The name comes from Ancient Greek εἴκοσι (eíkosi) 'twenty', and ἕδρα (hédra) 'seat'. The plural can be either "icosahedra" (/-drə/) or "icosahedrons".
There are infinitely many non-similar shapes of icosahedra, some of them being more symmetrical than others. The best known is the (convex, non-stellated) regular icosahedron—one of the Platonic solids—whose faces are 20 equilateral triangles.
^Jones, Daniel (2003) [1917], Peter Roach; James Hartmann; Jane Setter (eds.), English Pronouncing Dictionary, Cambridge: Cambridge University Press, ISBN 3-12-539683-2
In geometry, an icosahedron (/ˌaɪkɒsəˈhiːdrən, -kə-, -koʊ-/ or /aɪˌkɒsəˈhiːdrən/) is a polyhedron with 20 faces. The name comes from Ancient Greek εἴκοσι...
In geometry, the regular icosahedron (or simply icosahedron) is a convex polyhedron that can be constructed from pentagonal antiprism by attaching two...
In geometry, the truncated icosahedron is an Archimedean solid, one of 13 convex isogonal nonprismatic solids whose 32 faces are two or more types of...
In geometry, the great icosahedron is one of four Kepler–Poinsot polyhedra (nonconvex regular polyhedra), with Schläfli symbol {3,5⁄2} and Coxeter-Dynkin...
represented by its Schläfli symbol {5, 3}. The dual polyhedron is the regular icosahedron {3, 5}, having five equilateral triangles around each vertex. The convex...
cube, and dodecahedron and that the discovery of the octahedron and icosahedron belong to Theaetetus, a contemporary of Plato. In any case, Theaetetus...
perhaps only one has been found to be a true icosahedron, as opposed to a reinterpretation of the icosahedron dual, the dodecahedron. It is also possible...
In geometry, the triakis icosahedron is an Archimedean dual solid, or a Catalan solid, with 60 isosceles triangle faces. Its dual is the truncated dodecahedron...
In geometry, the metabidiminished icosahedron is one of the Johnson solids (J62). The name refers to one way of constructing it, by removing two pentagonal...
icosahedron is the outermost stellation of the icosahedron, and is "complete" and "final" because it includes all of the cells in the icosahedron's stellation...
In geometry, the tridiminished icosahedron is one of the Johnson solids (J63). The name refers to one way of constructing it, by removing three pentagonal...
Complete icosahedron may refer to: an icosahedron which has had none of its faces removed, as opposed to a partial icosahedron such as a geodesic hemisphere...
× Zuni Icosahedron is a Hong Kong-based international experimental theatre company. Founded in 1982, Zuni is one of the nine major professional performing...
uniform truncated icosahedron which has 12 pentagons, but only 20 hexagons. Truncated rhombic triacontahedron G(2,0) Truncated icosahedron G(1,1) cell-centered...
to 4.3 in). A Roman icosahedron has also been discovered after having long been misclassified as a dodecahedron. This icosahedron was excavated near Arloff...
The rhombic icosahedron is a polyhedron shaped like an oblate sphere. Its 20 faces are congruent golden rhombi; 3, 4, or 5 faces meet at each vertex....
{5}}}{3}}a^{3}&&\approx 41.615\,323\,782\,5a^{3}\end{aligned}}} If you expand an icosahedron by moving the faces away from the origin the right amount, without changing...
pyramids from an icosahedron: the pentagonal antiprism and metabidiminished icosahedron (two pyramids removed), and the tridiminished icosahedron (three pyramids...
In geometry, the great triambic icosahedron and medial triambic icosahedron (or midly triambic icosahedron) are visually identical dual uniform polyhedra...
its side and thus appears in the construction of the dodecahedron and icosahedron. A golden rectangle—that is, a rectangle with an aspect ratio of φ {\displaystyle...
In geometry, the rectified truncated icosahedron is a convex polyhedron. It has 92 faces: 60 isosceles triangles, 12 regular pentagons, and 20 regular...
polyhedral stellation or a compound. It can be seen as the compound of an icosahedron and dodecahedron. It is one of four compounds constructed from a Platonic...
considered as a parabidiminished icosahedron, a shape formed by removing two pentagonal pyramids from a regular icosahedron leaving two nonadjacent pentagonal...
In geometry, the truncated great icosahedron (or great truncated icosahedron) is a nonconvex uniform polyhedron, indexed as U55. It has 32 faces (12 pentagrams...
dodecahedron and icosahedron are dual polyhedra. A regular dodecahedron has 12 faces and 20 vertices, whereas a regular icosahedron has 20 faces and 12...
{5}}-1)E^{3}} It shares the same edge arrangement as the convex regular icosahedron; the compound with both is the small complex icosidodecahedron. If only...
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