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Net Stellation facets × 20 A net of a great stellated dodecahedron (surface geometry); twenty isosceles triangular pyramids, arranged like the faces of an icosahedron. It can be constructed as the third of three stellations of the dodecahedron, and referenced as Wenninger model [W22]. Complete net of a great stellated dodecahedron.
Great dodecahemicosacron (Dual of great dodecahemicosahedron) — V(5.6. 5 / 4 .6) π − π / 3 120° Small dodecahemicosacron (Dual of small dodecahemicosahedron) — V( 5 / 2 .6. 5 / 3 .6) π − π / 3 120° Great icosihemidodecacron (Dual of great icosihemidodecacron) — V(3. 10 / 3 . 3 / 2 ...
It can be seen as a polyhedron compound of a great icosahedron and great stellated dodecahedron. It is one of five compounds constructed from a Platonic solid or Kepler-Poinsot solid, and its dual. It is a stellation of the great icosidodecahedron. It has icosahedral symmetry (I h) and it has the same vertex arrangement as a great rhombic ...
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 icosahedron: Icosidodecahedron: Compound of cube and ...
The compound of small stellated dodecahedron and great dodecahedron is a polyhedron compound where the great dodecahedron is internal to its dual, the small stellated dodecahedron. This can be seen as one of the two three-dimensional equivalents of the compound of two pentagrams ({10/4} " decagram "); this series continues into the fourth ...
Small stellated dodecahedron: Great dodecahedron: 5|2 5 / 2 {5 / 2,5} I h: U34 K39 12 30 12 12{5 / 2} 21 Great dodecahedron: Small stellated dodecahedron: 5 / 2 |2 5 {5, 5 / 2} I h: U35 K40 12 30 12 12{5} 22 Great stellated dodecahedron: Great icosahedron: 3|2 5 / 2 {5 / 2,3} I h: U52 K57 20 30 12 12{5 / 2} 41 Great icosahedron (16th stellation ...
Schläfli also found four of the regular star 4-polytopes: the grand 120-cell, great stellated 120-cell, grand 600-cell, and great grand stellated 120-cell. He skipped the remaining six because he would not allow forms that failed the Euler characteristic on cells or vertex figures (for zero-hole tori: F − E + V = 2).
Kepler (1619) discovered two of the regular Kepler–Poinsot polyhedra, the small stellated dodecahedron and great stellated dodecahedron. Louis Poinsot (1809) discovered the other two, the great dodecahedron and great icosahedron. The set of four was proven complete by Augustin-Louis Cauchy in 1813 and named by Arthur Cayley in 1859.