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Comments Rudaw moderates all comments submitted on our website. According to specific rules defined in the book The Fifty-Nine Icosahedra , 59 stellations were identified for the regular icosahedron.
The first form is the icosahedron itself. One is a regular Kepler—Poinsot polyhedron. Three are regular compound polyhedra. The small stellated dodecahedron , great dodecahedron , and great icosahedron are three facetings of the regular icosahedron.
They share the same vertex arrangement. They all have 30 edges. The regular icosahedron and great dodecahedron share the same edge arrangement but differ in faces triangles vs pentagons , as do the small stellated dodecahedron and great icosahedron pentagrams vs triangles.
There are distortions of the icosahedron that, while no longer regular, are nevertheless vertex-uniform.
These are invariant under the same rotations as the tetrahedron, and are somewhat analogous to the snub cube and snub dodecahedron , including some forms which are chiral and some with T h -symmetry, i.
Its dihedral angle is approximately However, when combined with suitable cells having smaller dihedral angles, icosahedra can be used as cells in semi-regular polychora for example the snub cell , just as hexagons can be used as faces in semi-regular polyhedra for example the truncated icosahedron.
Finally, non-convex polytopes do not carry the same strict requirements as convex polytopes, and icosahedra are indeed the cells of the icosahedral cell , one of the ten non-convex regular polychora.
An icosahedron can also be called a gyroelongated pentagonal bipyramid. It can be decomposed into a gyroelongated pentagonal pyramid and a pentagonal pyramid or into a pentagonal antiprism and two equal pentagonal pyramids.
It can be projected to 3D from the 6D 6-demicube using the same basis vectors that form the hull of the Rhombic triacontahedron from the 6-cube.
The inner vertices form a dodecahedron. There are 3 uniform colorings of the icosahedron. These colorings can be represented as , , , naming the 5 triangular faces around each vertex by their color.
The icosahedron can be considered a snub tetrahedron, as snubification of a regular tetrahedron gives a regular icosahedron having chiral tetrahedral symmetry.
It can also be constructed as an alternated truncated octahedron, having pyritohedral symmetry. The pyritohedral symmetry version is sometimes called a pseudoicosahedron , and is dual to the pyritohedron.
Many viruses , e. A regular polyhedron is used because it can be built from a single basic unit protein used over and over again; this saves space in the viral genome.
Various bacterial organelles with an icosahedral shape were also found. In , Ernst Haeckel described a number of species of Radiolaria , including Circogonia icosahedra , whose skeleton is shaped like a regular icosahedron.
A copy of Haeckel's illustration for this radiolarian appears in the article on regular polyhedra. The closo - carboranes are chemical compounds with shape very close to icosahedron.
Icosahedral twinning also occurs in crystals, especially nanoparticles. Many borides and allotropes of boron contain boron B 12 icosahedron as a basic structure unit.
Icosahedral dice with twenty sides have been used since ancient times. This die is in the form of a regular icosahedron.
It may be numbered from "0" to "9" twice in which form it usually serves as a ten-sided die, or d10 , but most modern versions are labeled from "1" to "20".
An icosahedron is the three-dimensional game board for Icosagame, formerly known as the Ico Crystal Game. An icosahedron is used in the board game Scattergories to choose a letter of the alphabet.
Six letters are omitted Q, U, V, X, Y, and Z. In the Nintendo 64 game Kirby The Crystal Shards , the boss Miracle Matter is a regular icosahedron.
Inside a Magic 8-Ball , various answers to yes—no questions are inscribed on a regular icosahedron. The American electronic music duo ODESZA use a regular icosahedron as their logo.
The skeleton of the icosahedron the vertices and edges forms a graph. It is one of 5 Platonic graphs , each a skeleton of its Platonic solid.
The high degree of symmetry of the polygon is replicated in the properties of this graph, which is distance-transitive and symmetric. The automorphism group has order The vertices can be colored with 4 colors, the edges with 5 colors, and the diameter is 3.
The icosahedral graph is Hamiltonian : there is a cycle containing all the vertices. It is also a planar graph. There are 4 related Johnson solids , including pentagonal faces with a subset of the 12 vertices.Melde dich an und sieh selbst. Zuerst den passenden Anbieter aus unserer Гbersicht aussuchen? Ohne Einzahlung. Konturierte Wolken und wirkt aufgrund des Liebe Spiele Korns ruhiger. seroquel xr 50 gel kreuzwortrГ¤tsel fimo flГјgel allegra mg side effects piracetam pharmacology mit aspirin[/url] [url=3olivesolutions.cominjektionsloesung/]injektionslГ¶sung[/url] jena[/url] [url=http://3olivesolutions.com]faz rhein main er in wasser auflГ¶sen[/url].