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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
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
Regular icosahedron itself is the zeroth stellation of an icosahedron, and the subsequent stellation is obtained by radiating spikes from the faces of a regular icosahedron. The final stellation includes all of the cells in the icosahedron's stellation diagram, meaning every three intersecting face planes of the icosahedral core intersect ...
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.
Eighth stellation of icosahedron: 30 De 2 f 2: 3 6 8: 34 Ninth stellation: 13: Medial triambic icosahedron or Great triambic icosahedron: 31 De 2 f 2 g 2: 3 6 9' 11: 32 Ef 2 g 2: 5 6 9' 11: 33 f 1: 5' 6 ' 9 10: 35 Tenth stellation: Tenth stellation of icosahedron: 34 e 1 f 1: 3 ' 5 6 ' 9 10: 36 Eleventh stellation: Eleventh stellation of ...
Final stellation of the icosahedron, also called the "complete stellation of the icosahedron" In projective geometry , the complete icosahedron is a configuration of 20 planes and all their 3-fold (or higher) points of intersection (and optionally, depending on your understanding of a configuration, the various lines in space along which two ...
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 ...