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If the triangles are instead made to invert themselves and excavate the central icosahedron, the result is a great dodecahedron. The great stellated dodecahedron can be constructed analogously to the pentagram, its two-dimensional analogue, by attempting to stellate the n-dimensional pentagonal polytope which has pentagonal polytope faces and ...
Small stellated dodecahedron: Dodecahedron: Great stellated dodecahedron: Dodecahedron: Stellated octahedron: Octahedron: Compound of five octahedra: Icosahedron: Compound of five tetrahedra: Icosahedron: Small triambic icosahedron: Icosahedron: Great triambic icosahedron: Icosahedron: Compound of five cubes: Rhombic triacontahedron: Compound ...
This polyhedron can be considered a rectified great dodecahedron. It is center of a truncation sequence between a small stellated dodecahedron and great dodecahedron : The truncated small stellated dodecahedron looks like a dodecahedron on the surface, but it has 24 faces: 12 pentagons from the truncated vertices and 12 overlapping as ...
Compound of great icosahedron and stellated dodecahedron Type: stellation and compound: Coxeter diagram: ∪ : Convex hull: Dodecahedron: Polyhedra: 1 great icosahedron 1 great stellated dodecahedron: Faces: 20 triangles 12 pentagrams: Edges: 60 Vertices: 32 Symmetry group: icosahedral (I h)
This is an indexed list of the uniform and stellated polyhedra from the book Polyhedron Models, by Magnus Wenninger. The book was written as a guide book to building polyhedra as physical models. It includes templates of face elements for construction and helpful hints in building, and also brief descriptions on the theory behind these shapes.
In the second chapter is the earliest mathematical understanding of two types of regular star polyhedra, the small and great stellated dodecahedron; they would later be called Kepler's solids or Kepler Polyhedra and, together with two regular polyhedra discovered by Louis Poinsot, as the Kepler–Poinsot polyhedra. [7]
It is a stellation of the rhombic triacontahedron, and can also be called small stellated triacontahedron. Its dual is the dodecadodecahedron. Its 24 vertices are all on the 12 axes with 5-fold symmetry (i.e. each corresponds to one of the 12 vertices of the icosahedron). This means that on each axis there is an inner and an outer vertex.
The patterns {m/2, m} and {m, m/2} continue for odd m < 7 as polyhedra: when m = 5, we obtain the small stellated dodecahedron and great dodecahedron, [18] and when m = 3, the case degenerates to a tetrahedron. The other two Kepler–Poinsot polyhedra (the great stellated dodecahedron and great icosahedron) do not have regular hyperbolic tiling ...