Final stellation of the icosahedron - Wikipedia
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.
Icosahedron Stellations -- from Wolfram MathWorld
2024年10月10日 · Applying the stellation process to the icosahedron gives 20+30+60+20+60+120+12+30+60+60 cells of 11 different shapes and sizes (including the icosahedron itself). The icosahedron has 18 fully supported stellations, 16 of them reflexible and 2 of them chiral (Webb; where, as usual, the original icosahedron itself is …
Stellation - Wikipedia
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.
Stellations of the Icosahedron - Steve Dutch
2024年2月6日 · Each of the polygons enclosed by face intersections is a possible face of a stellation. We can identify 13 distinct faces as shown. Certain combinations of faces naturally occur together to enclose solids, which Coxeter termed cells. The different cells and their constituent faces are shown below.
Icosahedron Stellations - Michigan State University
The only Stellations of Platonic Solids which are Uniform Polyhedra are the three Dodecahedron Stellations the Great Icosahedron (stellation # 11).
Commentary on stellations and compounds of the Platonic solids
2015年8月5日 · It was known to the ancients, as is evident from the fact that it was used by the Pythagorean brotherhood as a symbol of health. Similarly a hexagon leads to a six-pointed star or hexagram (really not a single polygon but a compound of two equilateral triangles).
Final stellation of the icosahedron - WikiMili
In geometry, the complete or final stellation of the icosahedron 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.
Stellations of the Icosahedron - George W. Hart
Starting with the icosahedron, it turns out that there are 59 possible stellations. (Here we assuming some reasonable conditions, called Miller's rules, e.g., the resulting object should be finite, it should have the symmetries of the icosahedron, and we don't allow hollow centers that are not connected to the outside surface.
Tetrahedral Stellations of the Icosahedron - George W. Hart
There are 59 well-known stellations of the icosahedron which have full icosahedral symmetry. This page considers what happens when one relaxes the symmetry requirements and we look for fully-supported stellations of the icosahedron which have only tetrahedral symmetry.
Stellating the Icosahedron and Facetting the Dodecahedron
2020年12月19日 · Facetting is the reciprocal process to stellation, in which regions of a polyhedron are cut away to reveal new faces. There is a beautiful and perfectly symmetrical relationship between stellations of one polyhedron and facettings of another – in this case, the regular icosahedron and dodecahedron respectively.