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In geometry, the complete or final stellation of the icosahedron [1] is the outermost stellation of the icosahedron, and is "complete" and "final" because it includes all of the cells in the icosahedron's stellation diagram. That is, every three intersecting face planes of the icosahedral core intersect either on a vertex of this polyhedron or ...
Compound of dodecahedron and icosahedron: Icosidodecahedron: Compound of cube and octahedron: Cuboctahedron: Second stellation of the cuboctahedron [1] Cuboctahedron: Final stellation of the icosahedron: Icosahedron: Compound of ten tetrahedra: Icosahedron: Eighth stellation of the icosahedron: Icosahedron
The stellation process can be applied to higher dimensional polytopes as well. A stellation diagram of an n-polytope exists in an (n − 1)-dimensional hyperplane of a given facet. For example, in 4-space, the great grand stellated 120-cell is the final stellation of the regular 4-polytope 120-cell.
Small triambic icosahedron Medial triambic icosahedron Great triambic icosahedron Compound of five octahedra Compound of five tetrahedra Compound of ten tetrahedra Great icosahedron Excavated dodecahedron Final stellation; The stellation process on the icosahedron creates a number of related polyhedra and compounds with icosahedral symmetry
Fourth stellation of icosahedron: I h: 30 Fifth stellation of icosahedron: I h: 31 Sixth stellation of icosahedron: I h: 32 Seventh stellation of icosahedron: I h: 33 Eighth stellation of icosahedron: I h: 34 Ninth stellation of icosahedron Great triambic icosahedron: I h: 35 Tenth stellation of icosahedron: I 36 Eleventh stellation of ...
Small triambic icosahedron Medial triambic icosahedron Great triambic icosahedron Compound of five octahedra Compound of five tetrahedra Compound of ten tetrahedra Great icosahedron Excavated dodecahedron Final stellation; The stellation process on the icosahedron creates a number of related polyhedra and compounds with icosahedral symmetry
In geometry, the great triambic icosahedron and medial triambic icosahedron (or midly triambic icosahedron) are visually identical dual uniform polyhedra. The exterior surface also represents the De 2 f 2 stellation of the icosahedron. These figures can be differentiated by marking which intersections between edges are true vertices and which ...
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'.