124 relations: Chirality, Compound of eight octahedra with rotational freedom, Compound of eight triangular prisms, Compound of five cubes, Compound of five cuboctahedra, Compound of five cubohemioctahedra, Compound of five great cubicuboctahedra, Compound of five great dodecahedra, Compound of five great icosahedra, Compound of five great rhombihexahedra, Compound of five icosahedra, Compound of five nonconvex great rhombicuboctahedra, Compound of five octahedra, Compound of five octahemioctahedra, Compound of five rhombicuboctahedra, Compound of five small cubicuboctahedra, Compound of five small rhombihexahedra, Compound of five small stellated dodecahedra, Compound of five stellated truncated hexahedra, Compound of five tetrahedra, Compound of five tetrahemihexahedra, Compound of five truncated cubes, Compound of five truncated tetrahedra, Compound of four hexagonal prisms, Compound of four octahedra, Compound of four octahedra with rotational freedom, Compound of four triangular prisms, Compound of six cubes with rotational freedom, Compound of six decagonal prisms, Compound of six decagrammic prisms, Compound of six pentagonal antiprisms, Compound of six pentagonal prisms, Compound of six pentagrammic antiprisms, Compound of six pentagrammic crossed antiprisms, Compound of six pentagrammic prisms, Compound of six square antiprisms, Compound of six tetrahedra, Compound of six tetrahedra with rotational freedom, Compound of ten hexagonal prisms, Compound of ten octahedra, Compound of ten tetrahedra, Compound of ten triangular prisms, Compound of ten truncated tetrahedra, Compound of three cubes, Compound of three square antiprisms, Compound of twelve pentagonal antiprisms with rotational freedom, Compound of twelve pentagonal prisms, Compound of twelve pentagrammic antiprisms, Compound of twelve pentagrammic crossed antiprisms with rotational freedom, Compound of twelve pentagrammic prisms, ..., Compound of twelve tetrahedra with rotational freedom, Compound of twenty octahedra, Compound of twenty octahedra with rotational freedom, Compound of twenty tetrahemihexahedra, Compound of twenty triangular prisms, Compound of two great dodecahedra, Compound of two great icosahedra, Compound of two great inverted snub icosidodecahedra, Compound of two great retrosnub icosidodecahedra, Compound of two great snub icosidodecahedra, Compound of two icosahedra, Compound of two inverted snub dodecadodecahedra, Compound of two small stellated dodecahedra, Compound of two snub cubes, Compound of two snub dodecadodecahedra, Compound of two snub dodecahedra, Compound of two snub icosidodecadodecahedra, Compound of two tetrahedra, Compound of two truncated tetrahedra, Cube, Cuboctahedron, Cubohemioctahedron, Cyclic symmetry in three dimensions, Decagonal prism, Decagrammic prism, Dihedral symmetry in three dimensions, Great cubicuboctahedron, Great dodecahedron, Great icosahedron, Great inverted snub icosidodecahedron, Great retrosnub icosidodecahedron, Great rhombihexahedron, Great snub icosidodecahedron, Greatest common divisor, Group action, Hexagonal prism, Icosahedral symmetry, Icosahedron, Inverted snub dodecadodecahedron, Nonconvex great rhombicuboctahedron, Octahedral symmetry, Octahedron, Octahemioctahedron, Pentagonal antiprism, Pentagonal prism, Pentagrammic antiprism, Pentagrammic crossed-antiprism, Pentagrammic prism, Polyhedron, Polytope compound, Prismatic compound of antiprisms, Prismatic compound of antiprisms with rotational freedom, Prismatic compound of prisms, Prismatic compound of prisms with rotational freedom, Prismatic uniform polyhedron, Rhombicuboctahedron, Small cubicuboctahedron, Small rhombihexahedron, Small stellated dodecahedron, Snub cube, Snub dodecadodecahedron, Snub dodecahedron, Snub icosidodecadodecahedron, Square antiprism, Stellated truncated hexahedron, Subgroup, Symmetry group, Tetrahedral symmetry, Tetrahedron, Tetrahemihexahedron, Triangular prism, Truncated cube, Truncated tetrahedron, Uniform polyhedron. Expand index (74 more) »
Chirality
Chirality is a property of asymmetry important in several branches of science.
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Compound of eight octahedra with rotational freedom
This uniform polyhedron compound is a symmetric arrangement of 8 octahedra, considered as triangular antiprisms.
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Compound of eight triangular prisms
This uniform polyhedron compound is a symmetric arrangement of 8 triangular prisms, aligned in pairs with the axes of three-fold rotational symmetry of an octahedron.
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Compound of five cubes
The compound of five cubes is one of the five regular polyhedral compounds.
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Compound of five cuboctahedra
In geometry, this uniform polyhedron compound is a composition of 5 cuboctahedra.
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Compound of five cubohemioctahedra
This uniform polyhedron compound is a composition of 5 cubohemioctahedra, in the same arrangement as in the compound of 5 cuboctahedra.
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Compound of five great cubicuboctahedra
This uniform polyhedron compound is a composition of 5 great cubicuboctahedra, in the same arrangement as the compound of 5 truncated cubes.
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Compound of five great dodecahedra
This uniform polyhedron compound is a composition of 5 great dodecahedra, in the same arrangement as in the compound of 5 icosahedra.
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Compound of five great icosahedra
This uniform polyhedron compound is a composition of 5 great icosahedra, in the same arrangement as in the compound of 5 icosahedra.
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Compound of five great rhombihexahedra
This uniform polyhedron compound is a composition of 5 great rhombihexahedra, in the same vertex arrangement as the compound of 5 truncated cubes.
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Compound of five icosahedra
This uniform polyhedron compound is a composition of 5 icosahedra.
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Compound of five nonconvex great rhombicuboctahedra
This uniform polyhedron compound is a composition of 5 nonconvex great rhombicuboctahedra, in the same arrangement (i.e. sharing vertices with) the compound of 5 truncated cubes.
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Compound of five octahedra
The compound of five octahedra is one of the five regular polyhedron compounds.
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Compound of five octahemioctahedra
In geometry, this uniform polyhedron compound is a composition of 5 octahemioctahedra, in the same vertex arrangement as in the compound of 5 cuboctahedra.
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Compound of five rhombicuboctahedra
This uniform polyhedron compound is a composition of 5 rhombicuboctahedra, in the same vertex arrangement (i.e. sharing vertices with) the compound of 5 stellated truncated hexahedra.
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Compound of five small cubicuboctahedra
This uniform polyhedron compound is a composition of 5 small cubicuboctahedra, in the same vertex arrangement as the compound of 5 small rhombicuboctahedra.
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Compound of five small rhombihexahedra
This uniform polyhedron compound is a composition of 5 small rhombihexahedra, in the same vertex and edge arrangement as the compound of 5 small rhombicuboctahedra.
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Compound of five small stellated dodecahedra
This uniform polyhedron compound is a composition of 5 small stellated dodecahedra, in the same arrangement as in the compound of 5 icosahedra.
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Compound of five stellated truncated hexahedra
This uniform polyhedron compound is a composition of 5 stellated truncated hexahedra, formed by star-truncating each of the cubes in the compound of 5 cubes.
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Compound of five tetrahedra
The compound of five tetrahedra is one of the five regular polyhedral compounds.
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Compound of five tetrahemihexahedra
A compound of five tetrahemihexahedra is a uniform polyhedron compound and a symmetric arrangement of five tetrahemihexahedra.
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Compound of five truncated cubes
This uniform polyhedron compound is a composition of 5 truncated cubes, formed by truncating each of the cubes in the compound of 5 cubes.
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Compound of five truncated tetrahedra
This uniform polyhedron compound is a composition of 5 truncated tetrahedra, formed by truncating each of the tetrahedra in the compound of 5 tetrahedra.
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Compound of four hexagonal prisms
This uniform polyhedron compound is a symmetric arrangement of 4 hexagonal prisms, aligned with the axes of threefold rotational symmetry of an octahedron.
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Compound of four octahedra
This uniform polyhedron compound is a symmetric arrangement of 4 octahedra, considered as triangular antiprisms.
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Compound of four octahedra with rotational freedom
This uniform polyhedron compound is a symmetric arrangement of 4 octahedra, considered as triangular antiprisms.
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Compound of four triangular prisms
This uniform polyhedron compound is a chiral symmetric arrangement of 4 triangular prisms, aligned with the axes of three-fold rotational symmetry of an octahedron.
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Compound of six cubes with rotational freedom
This uniform polyhedron compound is a symmetric arrangement of 6 cubes, considered as square prisms.
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Compound of six decagonal prisms
This uniform polyhedron compound is a symmetric arrangement of 6 decagonal prisms, aligned with the axes of fivefold rotational symmetry of a dodecahedron.
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Compound of six decagrammic prisms
This uniform polyhedron compound is a symmetric arrangement of 6 decagrammic prisms, aligned with the axes of fivefold rotational symmetry of a dodecahedron.
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Compound of six pentagonal antiprisms
This uniform polyhedron compound is a symmetric arrangement of 6 pentagonal antiprisms.
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Compound of six pentagonal prisms
This uniform polyhedron compound is a chiral symmetric arrangement of 6 pentagonal prisms, aligned with the axes of fivefold rotational symmetry of a dodecahedron.
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Compound of six pentagrammic antiprisms
This uniform polyhedron compound is a chiral symmetric arrangement of 6 pentagrammic antiprisms, aligned with the axes of fivefold rotational symmetry of a dodecahedron.
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Compound of six pentagrammic crossed antiprisms
This uniform polyhedron compound is a symmetric arrangement of 6 pentagrammic crossed antiprisms.
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Compound of six pentagrammic prisms
This uniform polyhedron compound is a chiral symmetric arrangement of 6 pentagrammic prisms, aligned with the axes of fivefold rotational symmetry of a dodecahedron.
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Compound of six square antiprisms
This uniform polyhedron compound is a symmetric arrangement of 6 square antiprisms, aligned in pairs with the three axes of 4-fold rotational symmetry of a cube.
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Compound of six tetrahedra
This uniform polyhedron compound is a symmetric arrangement of 6 tetrahedra.
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Compound of six tetrahedra with rotational freedom
This uniform polyhedron compound is a symmetric arrangement of 6 tetrahedra, considered as antiprisms.
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Compound of ten hexagonal prisms
This uniform polyhedron compound is a symmetric arrangement of 10 hexagonal prisms, aligned with the axes of three-fold rotational symmetry of an icosahedron.
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Compound of ten octahedra
These uniform polyhedron compounds are symmetric arrangements of 10 octahedra, considered as triangular antiprisms, aligned with the axes of three-fold rotational symmetry of an icosahedron.
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Compound of ten tetrahedra
The compound of ten tetrahedra is one of the five regular polyhedral compounds.
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Compound of ten triangular prisms
This uniform polyhedron compound is a chiral symmetric arrangement of 10 triangular prisms, aligned with the axes of three-fold rotational symmetry of an icosahedron.
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Compound of ten truncated tetrahedra
This uniform polyhedron compound is a composition of 10 truncated tetrahedra, formed by truncating each of the tetrahedra in the compound of 10 tetrahedra.
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Compound of three cubes
This uniform polyhedron compound is a symmetric arrangement of 3 cubes, considered as square prisms.
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Compound of three square antiprisms
This uniform polyhedron compound is a symmetric arrangement of 3 square antiprisms, aligned with the three axes of 4-fold rotational symmetry of a cube.
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Compound of twelve pentagonal antiprisms with rotational freedom
This uniform polyhedron compound is a symmetric arrangement of 12 pentagonal antiprisms.
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Compound of twelve pentagonal prisms
This uniform polyhedron compound is a symmetric arrangement of 12 pentagonal prisms, aligned in pairs with the axes of fivefold rotational symmetry of a dodecahedron.
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Compound of twelve pentagrammic antiprisms
This uniform polyhedron compound is a symmetric arrangement of 12 pentagrammic antiprisms, aligned in pairs with the axes of fivefold rotational symmetry of a dodecahedron.
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Compound of twelve pentagrammic crossed antiprisms with rotational freedom
This uniform polyhedron compound is a symmetric arrangement of 12 pentagrammic crossed antiprisms.
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Compound of twelve pentagrammic prisms
This uniform polyhedron compound is a symmetric arrangement of 12 pentagrammic prisms, aligned in pairs with the axes of fivefold rotational symmetry of a dodecahedron.
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Compound of twelve tetrahedra with rotational freedom
This uniform polyhedron compound is a symmetric arrangement of 12 tetrahedra, considered as antiprisms.
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Compound of twenty octahedra
This uniform polyhedron compound is a symmetric arrangement of 20 octahedra (considered as triangular antiprisms).
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Compound of twenty octahedra with rotational freedom
This uniform polyhedron compound is a symmetric arrangement of 20 octahedra, considered as triangular antiprisms.
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Compound of twenty tetrahemihexahedra
This uniform polyhedron compound is a symmetric arrangement of 20 tetrahemihexahedra.
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Compound of twenty triangular prisms
This uniform polyhedron compound is a symmetric arrangement of 20 triangular prisms, aligned in pairs with the axes of three-fold rotational symmetry of an icosahedron.
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Compound of two great dodecahedra
This uniform polyhedron compound is a composition of 2 great dodecahedra, in the same arrangement as in the compound of 2 icosahedra.
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Compound of two great icosahedra
This uniform polyhedron compound is a composition of 2 great icosahedra, in the same arrangement as in the compound of 2 icosahedra.
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Compound of two great inverted snub icosidodecahedra
This uniform polyhedron compound is a composition of the 2 enantiomers of the great inverted snub icosidodecahedron.
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Compound of two great retrosnub icosidodecahedra
This uniform polyhedron compound is a composition of the 2 enantiomers of the great retrosnub icosidodecahedron.
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Compound of two great snub icosidodecahedra
This uniform polyhedron compound is a composition of the 2 enantiomers of the great snub icosidodecahedron.
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Compound of two icosahedra
This uniform polyhedron compound is a composition of 2 icosahedra.
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Compound of two inverted snub dodecadodecahedra
This uniform polyhedron compound is a composition of the 2 enantiomers of the inverted snub dodecadodecahedron.
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Compound of two small stellated dodecahedra
This uniform polyhedron compound is a composition of 2 small stellated dodecahedra, in the same arrangement as in the compound of 2 icosahedra.
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Compound of two snub cubes
This uniform polyhedron compound is a composition of the 2 enantiomers of the snub cube.
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Compound of two snub dodecadodecahedra
This uniform polyhedron compound is a composition of the 2 enantiomers of the snub dodecadodecahedron.
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Compound of two snub dodecahedra
This uniform polyhedron compound is a composition of the 2 enantiomers of the snub dodecahedron.
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Compound of two snub icosidodecadodecahedra
This uniform polyhedron compound is a composition of the 2 enantiomers of the snub icosidodecadodecahedron.
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Compound of two tetrahedra
In geometry, a compound of two tetrahedra is constructed by two overlapping tetrahedra, usually implied as regular tetrahedra.
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Compound of two truncated tetrahedra
This uniform polyhedron compound is a composition of two truncated tetrahedra, formed by truncating each of the tetrahedra in the stellated octahedron.
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Cube
In geometry, a cube is a three-dimensional solid object bounded by six square faces, facets or sides, with three meeting at each vertex.
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Cuboctahedron
In geometry, a cuboctahedron is a polyhedron with 8 triangular faces and 6 square faces.
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Cubohemioctahedron
In geometry, the cubohemioctahedron is a nonconvex uniform polyhedron, indexed as U15.
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Cyclic symmetry in three dimensions
In three dimensional geometry, there are four infinite series of point groups in three dimensions (n≥1) with n-fold rotational or reflectional symmetry about one axis (by an angle of 360°/n) does not change the object.
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Decagonal prism
In geometry, the decagonal prism is the eighth in the infinite set of prisms, formed by ten square side faces and two regular decagon caps.
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Decagrammic prism
In geometry, the decagrammic prism is one of an infinite set of nonconvex prisms formed by squares sides and two regular star polygon caps, in this case two decagrams.
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Dihedral symmetry in three dimensions
In geometry, dihedral symmetry in three dimensions is one of three infinite sequences of point groups in three dimensions which have a symmetry group that as abstract group is a dihedral group Dihn (n ≥ 2).
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Great cubicuboctahedron
In geometry, the great cubicuboctahedron is a nonconvex uniform polyhedron, indexed as U14.
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Great dodecahedron
In geometry, the great dodecahedron is a Kepler–Poinsot polyhedron, with Schläfli symbol and Coxeter–Dynkin diagram of.
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Great icosahedron
In geometry, the great icosahedron is one of four Kepler-Poinsot polyhedra (nonconvex regular polyhedra), with Schläfli symbol and Coxeter-Dynkin diagram of.
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Great inverted snub icosidodecahedron
In geometry, the great inverted snub icosidodecahedron is a uniform star polyhedron, indexed as U69.
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Great retrosnub icosidodecahedron
In geometry, the great retrosnub icosidodecahedron or great inverted retrosnub icosidodecahedron is a nonconvex uniform polyhedron, indexed as U74.
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Great rhombihexahedron
In geometry, the great rhombihexahedron is a nonconvex uniform polyhedron, indexed as U21.
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Great snub icosidodecahedron
In geometry, the great snub icosidodecahedron is a nonconvex uniform polyhedron, indexed as U57.
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Greatest common divisor
In mathematics, the greatest common divisor (gcd) of two or more integers, which are not all zero, is the largest positive integer that divides each of the integers.
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Group action
In mathematics, an action of a group is a formal way of interpreting the manner in which the elements of the group correspond to transformations of some space in a way that preserves the structure of that space.
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Hexagonal prism
In geometry, the hexagonal prism is a prism with hexagonal base.
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Icosahedral symmetry
A regular icosahedron has 60 rotational (or orientation-preserving) symmetries, and a symmetry order of 120 including transformations that combine a reflection and a rotation.
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Icosahedron
In geometry, an icosahedron is a polyhedron with 20 faces.
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Inverted snub dodecadodecahedron
In geometry, the inverted snub dodecadodecahedron is a nonconvex uniform polyhedron, indexed as U60.
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Nonconvex great rhombicuboctahedron
In geometry, the nonconvex great rhombicuboctahedron is a nonconvex uniform polyhedron, indexed as U17.
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Octahedral symmetry
A regular octahedron has 24 rotational (or orientation-preserving) symmetries, and a symmetry order of 48 including transformations that combine a reflection and a rotation.
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Octahedron
In geometry, an octahedron (plural: octahedra) is a polyhedron with eight faces, twelve edges, and six vertices.
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Octahemioctahedron
In geometry, the octahemioctahedron or allelotetratetrahedron is a nonconvex uniform polyhedron, indexed as U3.
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Pentagonal antiprism
In geometry, the pentagonal antiprism is the third in an infinite set of antiprisms formed by an even-numbered sequence of triangle sides closed by two polygon caps.
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Pentagonal prism
In geometry, the pentagonal prism is a prism with a pentagonal base.
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Pentagrammic antiprism
In geometry, the pentagrammic antiprism is one in an infinite set of nonconvex antiprisms formed by triangle sides and two regular star polygon caps, in this case two pentagrams.
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Pentagrammic crossed-antiprism
In geometry, the pentagrammic crossed-antiprism is one in an infinite set of nonconvex antiprisms formed by triangle sides and two regular star polygon caps, in this case two pentagrams.
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Pentagrammic prism
In geometry, the pentagrammic prism is one in an infinite set of nonconvex prisms formed by square sides and two regular star polygon caps, in this case two pentagrams.
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Polyhedron
In geometry, a polyhedron (plural polyhedra or polyhedrons) is a solid in three dimensions with flat polygonal faces, straight edges and sharp corners or vertices.
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Polytope compound
A polyhedral compound is a figure that is composed of several polyhedra sharing a common centre.
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Prismatic compound of antiprisms
In geometry, a prismatic compound of antiprism is a category of uniform polyhedron compound.
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Prismatic compound of antiprisms with rotational freedom
Each member of this infinite family of uniform polyhedron compounds is a symmetric arrangement of antiprisms sharing a common axis of rotational symmetry.
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Prismatic compound of prisms
Each member of this infinite family of uniform polyhedron compounds is a symmetric arrangement of prisms sharing a common axis of rotational symmetry.
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Prismatic compound of prisms with rotational freedom
Each member of this infinite family of uniform polyhedron compounds is a symmetric arrangement of prisms sharing a common axis of rotational symmetry.
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Prismatic uniform polyhedron
In geometry, a prismatic uniform polyhedron is a uniform polyhedron with dihedral symmetry.
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Rhombicuboctahedron
In geometry, the rhombicuboctahedron, or small rhombicuboctahedron, is an Archimedean solid with eight triangular and eighteen square faces.
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Small cubicuboctahedron
In geometry, the small cubicuboctahedron is a uniform star polyhedron, indexed as U13.
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Small rhombihexahedron
In geometry, the small rhombihexahedron is a nonconvex uniform polyhedron, indexed as U18.
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Small stellated dodecahedron
In geometry, the small stellated dodecahedron is a Kepler-Poinsot polyhedron, named by Arthur Cayley, and with Schläfli symbol.
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Snub cube
In geometry, the snub cube, or snub cuboctahedron, is an Archimedean solid with 38 faces: 6 squares and 32 equilateral triangles.
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Snub dodecadodecahedron
In geometry, the snub dodecadodecahedron is a nonconvex uniform polyhedron, indexed as U40.
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Snub dodecahedron
In geometry, the snub dodecahedron, or snub icosidodecahedron, is an Archimedean solid, one of thirteen convex isogonal nonprismatic solids constructed by two or more types of regular polygon faces.
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Snub icosidodecadodecahedron
In geometry, the snub icosidodecadodecahedron is a nonconvex uniform polyhedron, indexed as U46.
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Square antiprism
In geometry, the square antiprism is the second in an infinite set of antiprisms formed by an even-numbered sequence of triangle sides closed by two polygon caps.
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Stellated truncated hexahedron
In geometry, the stellated truncated hexahedron (or quasitruncated hexahedron) is a uniform star polyhedron, indexed as U19.
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Subgroup
In group theory, a branch of mathematics, given a group G under a binary operation ∗, a subset H of G is called a subgroup of G if H also forms a group under the operation ∗.
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Symmetry group
In group theory, the symmetry group of an object (image, signal, etc.) is the group of all transformations under which the object is invariant with composition as the group operation.
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Tetrahedral symmetry
A regular tetrahedron, an example of a solid with full tetrahedral symmetry A regular tetrahedron has 12 rotational (or orientation-preserving) symmetries, and a symmetry order of 24 including transformations that combine a reflection and a rotation.
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Tetrahedron
In geometry, a tetrahedron (plural: tetrahedra or tetrahedrons), also known as a triangular pyramid, is a polyhedron composed of four triangular faces, six straight edges, and four vertex corners.
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Tetrahemihexahedron
In geometry, the tetrahemihexahedron or hemicuboctahedron is a uniform star polyhedron, indexed as U4.
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Triangular prism
In geometry, a triangular prism is a three-sided prism; it is a polyhedron made of a triangular base, a translated copy, and 3 faces joining corresponding sides.
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Truncated cube
In geometry, the truncated cube, or truncated hexahedron, is an Archimedean solid.
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Truncated tetrahedron
In geometry, the truncated tetrahedron is an Archimedean solid.
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Uniform polyhedron
A uniform polyhedron is a polyhedron which has regular polygons as faces and is vertex-transitive (transitive on its vertices, isogonal, i.e. there is an isometry mapping any vertex onto any other).
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Redirects here:
Uniform Compounds of Uniform Polyhedra, Uniform polyhedral compound.
References
[1] https://en.wikipedia.org/wiki/Uniform_polyhedron_compound