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Icosahedron: Small triambic icosahedron: Icosahedron: Great triambic icosahedron: Icosahedron: Compound of five cubes: Rhombic triacontahedron: Compound of great icosahedron and great stellated dodecahedron: Icosidodecahedron: Compound of great icosahedron and great stellated dodecahedron: Great icosidodecahedron: Compound of dodecahedron and ...
In Wenninger's book Polyhedron Models, the final stellation of the icosahedron is included as the 17th model of stellated icosahedra with index number W 42. [ 7 ] In 1995, Andrew Hume named it in his Netlib polyhedral database as the echidnahedron after the echidna or spiny anteater, a small mammal that is covered with coarse hair and spines ...
The stellation diagram for the icosahedron with the central triangle marked for the original icosahedron. The Fifty-Nine Icosahedra is a book written and illustrated by H. S. M. Coxeter, P. Du Val, H. T. Flather and J. F. Petrie.
(Triakis icosahedron) I h: 27 Second stellation of icosahedron: I h: 28 Excavated dodecahedron (Third stellation of icosahedron) I h: 29 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 ...
There are 58 stellations of the icosahedron, including the great icosahedron (one of the Kepler–Poinsot polyhedra), and the second and final stellations of the icosahedron. The 59th model in The fifty nine icosahedra is the original icosahedron itself. Many "Miller stellations" cannot be obtained directly by using Kepler's method.
The truncated great stellated dodecahedron is a degenerate polyhedron, with 20 triangular faces from the truncated vertices, and 12 (hidden) doubled up pentagonal faces ({10/2}) as truncations of the original pentagram faces, the latter forming two great dodecahedra inscribed within and sharing the edges of the icosahedron.
In geometry, a tetrahedrally diminished [a] dodecahedron (also tetrahedrally stellated icosahedron or propello tetrahedron [1]) is a topologically self-dual polyhedron made of 16 vertices, 30 edges, and 16 faces (4 equilateral triangles and 12 identical quadrilaterals).
The regular icosahedron can be faceted into three regular Kepler–Poinsot polyhedra: small stellated dodecahedron, great dodecahedron, and great icosahedron. They all have 30 edges. They all have 30 edges.