Revision #627 → #1476 · back to history
addedPlatonic solidd990e1749de3
addedRegular polyhedron4b98b7cef895
addedExactly five Platonic solidsee9866f72aea
addedTetrahedron vertices half of cubebefc51bec333
addedDodecahedron vertices shared with cubebbe06567fef2
addedCombinatorial characterization of Platonic solids1cbabf3fdf30
addedSchläfli symbol485c6c74cc6c
addedEdge incidence relation pF=2E=qV2453fbd408f0
addedEuler's formulae63a3796c5fc
addedV, E, F determined by p and q2e485a1bdc13
addedSwapping p and q interchanges F and Vdc02a5022dcd
addedOnly five convex regular polyhedra exist8767aa238ada
addedAngle defectea05df933361
addedVertex angle sum less than 360°820a9c822ec9
addedOnly five possibilities for {p,q}65ceb1c28830
addedDihedral angle6f2f4b31fb6a
addedDihedral angle formula8b1f75ada295
addedCoxeter number3cadd2421522
addedAngular deficiency21cc123b128f
addedDefect formula6534dc3d67a9
addedDescartes' total angular defect theoremc3d34798682c
addedSolid angle52180ce3cfe3
addedVertex solid angle formulafb8e38587292
addedSolid angle of a face926d169669f8
addedThree concentric spheres488676ffe924
addedCircumradius, midradius, inradius07b76fe4aae2
addedCircumradius and inradius formulasfbf67c07a6a3
addedMidradius formula6bd18fb27d6b
addedCircumradius/inradius ratio symmetric in p,qb284f5d57bb3
addedSurface area formula7a3ba27c6995
addedVolume formulad24bde5cdaa8
addedBest sphere approximationef6a5edb7a20
addedDistance identity for all five solids127b6595318c
addedDistances from circumscribed sphere pointf3a22c266903
addedRupert property5d509232d00d
addedAll Platonic solids are Ruperte12d63c25ed1
addedDual polyhedron51596d3dd3e1
addedDual of a Platonic solid is Platonicf1d2884e259e
addedTetrahedron is self-dualed48960c2f08
addedCube–octahedron dual pair536996661095
addedDodecahedron–icosahedron dual paird4f140b7da1c
addedDual Schläfli symbola8e603f5517c
addedRadii relation under dualization8195487a1e15
addedSymmetry group of a polyhedroncd73ae98fb80
addedOrder of the symmetry group014421364b2c
addedRegularity via uniformity891c3214b5d6
addedOnly three symmetry groupsce0b0c519c35
addedOrders of rotation groupsfac2a6d75e60
addedCentral symmetry except tetrahedron87b967991943
addedKepler–Poinsot polyhedra4c24b8a9b915
addedCuboctahedron and icosidodecahedronc949f6d72248
addedArchimedean solids90a56dca388c
addedCatalan solids38b134646399
addedUniform polyhedra950d160041dc
addedJohnson solids7f6691ee3d77
addedConvex deltahedra0c17babd820f
addedPlatonic solids as sphere tessellationsf5c7b3a70793
addedHosohedra and dihedra50f3862d12b4
addedSphere tessellation condition8f154c3f78d5
addedPlane tessellation condition8e55472f3d56
addedHyperbolic tessellation condition36d6a7c86faa
addedPolyhedra generalize to polytopesf324a59ce3ae
addedSix convex regular 4-polytopes75a782ccf4ab
addedThree convex regular polytopes above dimension four914e4b2279b7