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    Pyramid

    Polyhedra with available data

    equilateral square pyramid | equilateral pentagonal pyramid | regular tetrahedron

    Visual representations

    Visual representations

    Alternate names

    1-Johnson solid | 2-Zalgaller polyhedron | 4-pyramid

    2-Johnson solid | 3-Zalgaller polyhedron | 5-pyramid

    1-uniform dual polyhedron | 1-uniform polyhedron | 1-Zalgaller polyhedron | 3-canonical pyramid | 3-pyramid | 3-simplex | tetrahedron | three-simplex | triangular pyramid

    Combinatorial properties

    | vertices | edges | faces equilateral square pyramid | 5 | 8 | 5 (4 triangles, 1 quadrilateral) equilateral pentagonal pyramid | 6 | 10 | 6 (5 triangles, 1 pentagon) regular tetrahedron | 4 | 6 | 4 (4 triangles)

    Edge lengths

    1 (8 edges)

    1 (10 edges)

    1 (6 edges)

    Geometric properties

    | volume equilateral square pyramid | 1/(3 sqrt(2)) equilateral pentagonal pyramid | 1/24 (5 + sqrt(5)) regular tetrahedron | 1/(6 sqrt(2)) | surface area equilateral square pyramid | 1 + sqrt(3) equilateral pentagonal pyramid | 1/2 sqrt(5/2 (10 + sqrt(5) + sqrt(75 + 30 sqrt(5)))) regular tetrahedron | sqrt(3) | circumradius equilateral square pyramid | 1/sqrt(2) equilateral pentagonal pyramid | 1/2 sqrt(1/2 (5 + sqrt(5))) regular tetrahedron | sqrt(3/2)/2 | midradius equilateral square pyramid | 1/2 equilateral pentagonal pyramid | Ï•/2 regular tetrahedron | 1/(2 sqrt(2)) | inradius equilateral square pyramid | 1/(sqrt(2) + sqrt(6)) equilateral pentagonal pyramid | root of 6400 x^8 - 27200 x^6 + 2960 x^4 - 100 x^2 + 1 near x = 0.232788 regular tetrahedron | 1/(2 sqrt(6)) (assuming unit edge lengths)

    Schläfli symbol

    | regular tetrahedron Schläfli symbol | {3, 3}

    Wythoff symbol

    | regular tetrahedron Wythoff symbol | 3|2 3

    Nets

    Nets

    Skeleton graphs

    | skeleton graph name equilateral square pyramid | 5-wheel graph equilateral pentagonal pyramid | 6-wheel graph regular tetrahedron | tetrahedral graph

    Dual polyhedra

    | dual name regular tetrahedron | tetrahedron

    Dual skeleton graphs

    | dual skeleton name equilateral square pyramid | 5-wheel graph equilateral pentagonal pyramid | 6-wheel graph regular tetrahedron | tetrahedral graph

    Symmetry group

    | equilateral square pyramid | equilateral pentagonal pyramid | regular tetrahedron symmetry group | point group C_4v | point group C_5v | tetrahedral group

    Common properties

    amphichiral | canonical | convex | equilateral | pyramid | rigid | self-dual | simple | Zalgaller

    Associated people

    Plato

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