Polyhedron of the Day @dailypolyhedra - Tumblr Blog

Daily Polyhedra Archive

(An ongoing list of polyhedra that have already been covered by this blog, mostly for my own convenience. This is a work-in-progress.)

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Polyhedron of the Day #345: Elongated pentagonal bipyramid

The elongated pentagonal bypyramid (also known as the elongated pentagonal dipyramid or bicapped pentagonal prism) is a Johnson solid (J16). It has 15 faces (10 triangles, 5 squares), 25 edges, and 12 vertices. It is created by attaching pentagonal pyramids to the bases of a pentagonal prism. Its dual is the pentagonal bifrustum.

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Polyhedron of the Day #344: First noble kizippergrammic hexecontahedron

The first noble kizippergrammic hexecontahedron is a noble polyhedron. It has 60 faces (all irregular hexagons), 180 edges, and 60 vertices. Its genus is 62. It shares its vertex arrangement with the small snub icosicosidodecahedron. Its dual is the noble kiunihexagrammic hexecontahedron.

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Polyhedron of the Day #343: Canonical joined truncated icosahedron

The canonical joined truncated icosahedron has 90 faces (60 kites, 30 rhombi), 180 edges, and 92 vertices.

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Polyhedron of the Day #342: Gyrated blend of truncated dodecahedra

The gyrated blend of truncated dodecahedra is a toroidal polyhedron with 60 faces (40 triangles, 20 decagons), 160 edges, and 100 vertices. It can be constructed by blending two truncated dodecahedra. It is a 10-10-3 acrohedron.

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Polyhedron of the Day #341: Icositruncated dodecadodecahedron

The icositruncated dodecadodecahedron (also known as the icosidodecatruncated icosidodecahedron) is a uniform star polyhedron. It has 44 faces (20 hexagons, 12 decagons, 12 decagrams), 180 edges, and 120 vertices. Its dual is the tridyakis icosahedron.

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Polyhedron of the Day #340: Sesquitruncated rhombic dodecahedron

The sesquitruncated rhombic dodecahedron is a near-miss Johnson solid. It has 50 faces (32 triangles, 6 squares, 12 decagons), 120 edges, and 72 vertices. It is constructed by inscribing a decagon in each face of the rhombic dodecahedron, and then filling in remaining gaps with triangles and squares.

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Polyhedron of the Day #339: Great heptagrammic pyramid

The great heptagrammic pyramid is a pyramidal polyhedron. It has 8 faces (7 triangles, 1 great heptagram), 14 edges, and 8 vertices. It is self-dual.

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Polyhedron of the Day #338: Elongated triangular bipyramid

The elongated triangular bipyramid (also known as the elongated triangular dipyramid or triakis triangular prism) is a Johnson solid (J14). It has 9 faces (6 triangles, 3 squares), 15 edges, and 8 vertices. It is created by attaching a tetrahedron to each of the bases of a triangular prism. Its dual is the triangular bifrustum.

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Polyhedron of the Day #337: Excavated great icosahedron

The excavated great icosahedron is an isohedral deltahedron. It has 60 faces (all triangles), 90 edges, and 32 vertices. It is constructed by excavating each face of the great icosahedron with a tetrahedron. Its dual is a semi-uniform quasitruncated great stellated dodecahedron.

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Polyhedron of the Day #336: Octagrammic concave trapezohedron

The octagrammic concave trapezohedron has 16 faces (all darts), 32 edges, and 18 vertices. Its dual is the octagrammic crossed antiprism.

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Polyhedron of the Day #335: Compound of three square antiprisms

The compound of three square antiprisms (also known as the great snub cube) is a uniform polyhedral compound. It has 30 faces (24 triangles, 6 squares), 48 edges, and 24 vertices. It is chiral. Its dual is the compound of three square antitegums.

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Polyhedron of the Day #334: Small rhombidodecahedron

The small rhombidodecahedron is a uniform star polyhedron with 42 faces (30 squares, 12 decagons), 120 edges, and 60 vertices. It has the same vertex arrangement as the small stellated truncated dodecahedron and the uniform compounds of 6 and 12 pentagrammic prisms. It shares its edge arrangement with the rhombicosidodecahedron and the small dodecicosidodecahedron. Its dual is the small rhombidodecacron.

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Polyhedron of the Day #333: Decagrammic prism

The decagrammic prism is a prismatic uniform polyhedron. It has 12 faces (2 decagrams, 10 squares), 30 edges, and 20 vertices. Its dual is the decagrammic bipyramid.

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Polyhedron of the Day #332: Z4

Z4 (in Stewart notation) is non-convex regular faced polyhedron. It has 22 faces (2 squares, 20 triangles), 34 edges, and 14 vertices. It is used in the construction of many Stewart toroids.

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Polyhedron of the Day #331: Gyroelongated square pyramid

The gyroelongated square pyramid is a Johnson Solid (J10). It has 13 faces (12 triangles, 1 square), 20 edges, and 9 vertices. It can be constructed by attaching an equilateral square pyramid to a square antiprism.

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Polyhedron of the Day #330: Canonical snub icosidodecahedron

The canonical snub icosidodecahedron has 182 faces (140 triangles, 30 rhombi, 12 pentagons), 300 edges, and 120 vertices. It is chiral.

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