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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.
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
Only a few of his models were of icosahedra. His names are given in shortened form, with "... of the icosahedron" left off. Wheeler. Wheeler found his figures, or "forms" of the icosahedron, by selecting line segments from the stellation diagram. He carefully distinguished this from Kepler's classical stellation process. Coxeter et al. ignored ...
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 ...
[3] [4] The shapes first studied in this book include the final stellation of the icosahedron and the compound of three octahedra, made famous by M. C. Escher's print Stars. [5] Joseph Malkevitch lists the publication of this book, which documented all that was known on polyhedra at the time, as one of 25 milestones in the history of polyhedra.