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After teaching at a grammar school in Zittau, he moved to the gymnasium in Bautzen. Escher's print Stars. Joseph Malkevitch lists the publication of this book, which documented all, known on polyhedra at the time, as one of 25 milestones in the history of polyhedra. Malkevitch writes that the book's "beautiful pictures of uniform polyhedra In — he donated his model collection to Heidelberg University , the university in turn gave him an honorary doctorate in It is composed of 20 intersecting triangular faces, having five triangles meeting at each vertex in a pentagrammic sequence; the great icosahedron can be constructed analogously to the pentagram , its two-dimensional analogue, via the extension of the -D simplex faces of the core nD polytope until the figure regains regular faces.

The grand cell can be seed as its four-dimensional analogue using the same process; the great icosahedron can be constructed a uniform snub, with different colored faces and only tetrahedral symmetry:. This construction can be called a retrosnub tetrahedron or retrosnub tetratetrahedron , similar to the snub tetrahedron symmetry of the icosahedron, as a partial faceting of the truncated octahedron :, it can be constructed with 2 colors of triangles and pyritohedral symmetry as, or, is called a retrosnub octahedron.

It shares the same vertex arrangement as the regular convex icosahedron. It shares the same edge arrangement as the small stellated dodecahedron.

A truncation operation applied to the great icosahedron, produces a sequence of uniform polyhedra. Truncating edges down to points produces the great icosidodecahedron as a rectified great icosahedron; the process completes as a birectification , reducing the original faces down to points, producing the great stellated dodecahedron. The truncated great stellated dodecahedron is a degenerate polyhedron , with 20 triangular faces from the truncated vertices, 12 doubled up pentagonal faces as truncations of the original pentagram faces, the latter forming two great dodecahedra inscribed within and sharing the edges of the icosahedron.

Wenninger, Magnus.

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Polyhedron Models. Cambridge University Press.