## Regular polytopes |

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#### Review: Regular Polytopes

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### Contents

Regular quasiregular and rhombic solids | 3 |

REGULAR AND QUASIREGULAR SOLIDS | 15 |

Some equilateral zonohedra | 29 |

23 other sections not shown

### Common terms and phrases

a-form analogous belong bounding hyperplanes branches cells centre circum-radius compound congruent transformation convex coordinates corresponding cos2 Coxeter cross polytope cube cuboctahedron defined denote dihedral angle direct dodecahedron edges elements equal equation equatorial polygon Euclidean simplexes Euler's Formula eutactic faces fact finite groups follows four dimensions four-dimensional fundamental region Gosset graph half-turn hedron Hence hyperplanes icosahedron infinite inscribed integers invariant ir/p lattice lines measure polytope mid-points modified Petrie polygon nodes number of dimensions obtain octahedra octahedron orthoscheme P0 Pi parallel pentagonal permutations perpendicular Petrie polygon planes of symmetry Platonic solids polyhedra polytope or honeycomb positive semidefinite projection pyramids reciprocal reflections regular polyhedron regular polytope rhombs Ri R2 rotation group Schlafli symbol Schoute sections segments sides skew polygon space sphere spherical simplex star star-polytopes stellated subgroup symmetry group tetrahedron theorem triangles truncation vectors vertex figure w-dimensional zonohedron