Regular Polytopes |
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according alternate angle belong bounding branches called cells centre Chapter circles compound congruent connected consider consists construction contains coordinates corresponding cube defined definite derived determined dihedral angle dimensions direct dodecahedron edges elements equal equation Euclidean expression faces fact finite five follows formula four fundamental region given graph Hence honeycomb hyperplanes icosahedron infinite instance invariant joining kind lines lines of symmetry means nodes obtain occur octahedron operations opposite orthogonal pairs parallel particular permutations perpendicular Petrie polygon plane polyhedra polyhedron polytope positive possible projection R₁ R₂ rational reciprocal reflections regarded regular regular polytope relation remaining represent respective result rotation Schläfli shows sides simplex solid space sphere spherical square star subgroup surface symbol symmetry symmetry group Table tessellation tetrahedron transformation triangles values vectors vertex figure vertices