an icosahedron which has had none of its faces removed, as opposed to a partial icosahedron such as a geodesic hemisphere
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 planes meet)
Topics referred to by the same term
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Completeicosahedron may refer to: an icosahedron which has had none of its faces removed, as opposed to a partial icosahedron such as a geodesic hemisphere...
In geometry, the complete or final stellation of the icosahedron is the outermost stellation of the icosahedron, and is "complete" and "final" because...
In geometry, the truncated icosahedron is an Archimedean solid with 32 faces. It is a polyhedron that may associated with footballs (soccer balls) typically...
In geometry, the great icosahedron is one of four Kepler–Poinsot polyhedra (nonconvex regular polyhedra), with Schläfli symbol {3,5⁄2} and Coxeter-Dynkin...
its side and thus appears in the construction of the dodecahedron and icosahedron. A golden rectangle—that is, a rectangle with an aspect ratio of φ {\displaystyle...
the great icosahedron, is related in a similar fashion to the icosahedron. Shaving the triangular pyramids off results in an icosahedron. If the pentagrammic...
tensegrity icosahedron. This choice of parameters gives the vertices the positions of Jessen's icosahedron; they are different from the regular icosahedron, for...
{5}}-1)E^{3}} It shares the same edge arrangement as the convex regular icosahedron; the compound with both is the small complex icosidodecahedron. If only...
cube, and dodecahedron and that the discovery of the octahedron and icosahedron belong to Theaetetus, a contemporary of Plato. In any case, Theaetetus...
hull of two opposite edges of a regular icosahedron forms a golden rectangle. The twelve vertices of the icosahedron can be decomposed in this way into three...
between the cube and the octahedron, and between the dodecahedron and the icosahedron. Also, partially because the tetrahedron is self-dual, only one Archimedean...
the regular icosahedron, the Jessen's icosahedron, and the regular octahedron, in accordance with the pyritohedral symmetry of the icosahedron. When interpreted...
previous stages, it is possible to complete one stage in such a way that the next stage is also already complete. This is known as a "skip", commonly...
be realized by linked ellipses, or (using the vertices of a regular icosahedron) by linked golden rectangles. It is impossible to realize them using...
arrangement as the convex regular icosahedron. It also shares the same edge arrangement with the great icosahedron, with which it forms a degenerate uniform...
the formula C60. It has a cage-like fused-ring structure (truncated icosahedron) made of twenty hexagons and twelve pentagons, and resembles a football...
Building a pyramid on each face of a regular icosahedron requires 30 units, and results in a triakis icosahedron. Uniform polyhedra can be adapted to Sonobe...
snub polyhedra, not including the antiprisms, the icosahedron as a snub tetrahedron, the great icosahedron as a retrosnub tetrahedron and the great disnub...
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