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The complete icosahedron is formed from all the cells in the stellation, but only the outermost regions, labelled "13" in the diagram, are visible. The stellation of a polyhedron extends the faces of a polyhedron into infinite planes and generates a new polyhedron that is bounded by these planes as faces and the intersections of these planes as ...
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.
The great icosahedron and its dual resemble the icosahedron and its dual in that they have faces and vertices on the 3-fold (yellow) and 5-fold (red) symmetry axes. In the great dodecahedron and its dual all faces and vertices are on 5-fold symmetry axes (so there are no yellow elements in these images).
A stellated icosahedron made from custom papers Modular origami or unit origami is a multi-stage paper folding technique in which several, or sometimes many, sheets of paper are first folded into individual modules or units and then assembled into an integrated flat shape or three-dimensional structure, usually by inserting flaps into pockets ...
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.
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 1858, Bertrand derived the regular star polyhedra (Kepler–Poinsot polyhedra) by faceting the regular convex icosahedron and dodecahedron. In 1974, Bridge enumerated the more straightforward facetings of the regular polyhedra, including those of the dodecahedron. In 2006, Inchbald described the basic theory of faceting diagrams for polyhedra.
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).