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- Polyhedral compounds

Compound of five cubes

The compound of five cubes is one of the five regular polyhedral compounds. It was first described by Edmund Hess in 1876. It is one of five regular compounds, and dual to the compound of five octahed

Compound of 5-cube and 5-orthoplex

In 5-dimensional geometry, the 5-cube 5-orthoplex compound is a polytope compound composed of a regular 5-cube and dual regular 5-orthoplex. A compound polytope is a figure that is composed of several

Compound of six tetrahedra

The compound of six tetrahedra is a uniform polyhedron compound. It's composed of a symmetric arrangement of 6 tetrahedra. It can be constructed by inscribing a stella octangula within each cube in th

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. It arises from superimposing two copies of th

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.

Compound of great icosahedron and great stellated dodecahedron

There are two different compounds of great icosahedron and great stellated dodecahedron: one is a dual compound and a stellation of the great icosidodecahedron, the other is a stellation of the icosid

Polytope compound

In geometry, a polyhedral compound is a figure that is composed of several polyhedra sharing a common centre. They are the three-dimensional analogs of polygonal compounds such as the hexagram. The ou

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.

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.

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.

Small complex rhombicosidodecahedron

In geometry, the small complex rhombicosidodecahedron (also known as the small complex ditrigonal rhombicosidodecahedron) is a degenerate uniform star polyhedron. It has 62 faces (20 triangles, 12 pen

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. It also results from composing the two enant

Compound of five icosahedra

The compound of five icosahedra is uniform polyhedron compound. It's composed of 5 icosahedra, rotated around a common axis. It has icosahedral symmetry Ih. The triangles in this compound decompose in

Great complex icosidodecahedron

In geometry, the great complex icosidodecahedron is a degenerate uniform star polyhedron. It has 12 vertices, and 60 (doubled) edges, and 32 faces, 12 pentagrams and 20 triangles. All edges are double

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. It results from composing the two

Compound of six cubes with rotational freedom

This uniform polyhedron compound is a symmetric arrangement of 6 cubes, considered as square prisms. It can be constructed by superimposing six identical cubes, and then rotating them in pairs about t

Compound of three tetrahedra

In geometry, a compound of three tetrahedra can be constructed by three tetrahedra rotated by 60 degree turns along an axis of the middle of an edge. It has dihedral symmetry, D3d, order 12. It is a u

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. This infinite family can be enumerated as follows

Compound of octahedra

A compound of octahedra may be:
* Compound of two octahedra
* Compound of three octahedra
* Also Compound of three triangular antiprisms
* Compound of four octahedra
* More generally, Compound of

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.

Compound of four cubes

The compound of four cubes or Bakos compound is a face-transitive polyhedron compound of four cubes with octahedral symmetry. It is the dual of the compound of four octahedra. Its surface area is 687/

Compound of two inverted snub dodecadodecahedra

The compound of two inverted snub dodecadodecahedra is a uniform polyhedron compound. It's composed of the 2 enantiomers of the inverted snub dodecadodecahedron.

Compound of eight octahedra with rotational freedom

The compound of eight octahedra with rotational freedom is a uniform polyhedron compound. It is composed of a symmetric arrangement of 8 octahedra, considered as triangular antiprisms. It can be const

Compound of twelve tetrahedra with rotational freedom

This uniform polyhedron compound is a symmetric arrangement of 12 tetrahedra, considered as antiprisms. It can be constructed by superimposing six identical copies of the stella octangula, and then ro

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.

Compound of six tetrahedra with rotational freedom

The compound of six tetrahedra with rotational freedom is a uniform polyhedron compound made of a symmetric arrangement of 6 tetrahedra, considered as antiprisms. It can be constructed by superimposin

Compound of twenty octahedra with rotational freedom

The compound of twenty octahedra with rotational freedom is a uniform polyhedron compound. It's composed of a symmetric arrangement of 20 octahedra, considered as triangular antiprisms. It can be cons

Compound of two snub icosidodecadodecahedra

The compound of two snub icosidodecadodecahedra is a uniform polyhedron compound. It's composed of the 2 enantiomers of the snub icosidodecadodecahedron.

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. It arises from superimposing two copies of the co

Compound of six octahedra

The compound of six octahedra has two forms. One form is a symmetric arrangement of 6 octahedra, considered as square bipyramid. It is a dual of a special case of the compound of 6 cubes with rotation

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. It results from composing the t

Compound of five truncated tetrahedra

The compound of five truncated tetrahedra is a uniform polyhedron compound. It's composed of 5 truncated tetrahedra rotated around a common axis. It may be formed by truncating each of the tetrahedra

Compound of five tetrahemihexahedra

A compound of five tetrahemihexahedra is a uniform polyhedron compound and a symmetric arrangement of five tetrahemihexahedra. It is chiral with icosahedral symmetry (I).

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. It is related to the cantic cube construction of

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.

Compound of four octahedra

The compound of four octahedra is a uniform polyhedron compound. It's composed of a symmetric arrangement of 4 octahedra, considered as triangular antiprisms. It can be constructed by superimposing fo

Compound of tetrahedra

A compound of tetrahedra might be:
* Compound of two tetrahedra – stellated octahedron
* Compound of three tetrahedra
* Compound of four tetrahedra
* Compound of five tetrahedra
* Compound of six

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. It is one of only five polyhedral compounds (along with the compou

Compound of two snub dodecahedra

This uniform polyhedron compound is a composition of the 2 enantiomers of the snub dodecahedron. The vertex arrangement of this compound is shared by a convex nonuniform truncated icosidodecahedron, w

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. It is one of only five polyhedral compounds (along with

Compound of two great snub icosidodecahedra

This uniform polyhedron compound is a composition of the 2 enantiomers of the great snub icosidodecahedron.

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. It is one of only five polyhedral compounds (along with the compou

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. It results from composing the two

Compound of three octahedra

In mathematics, the compound of three octahedra or octahedron 3-compound is a polyhedral compound formed from three regular octahedra, all sharing a common center but rotated with respect to each othe

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.

Stellated octahedron

The stellated octahedron is the only stellation of the octahedron. It is also called the stella octangula (Latin for "eight-pointed star"), a name given to it by Johannes Kepler in 1609, though it was

Compound of cubes

There is one regular compound of cubes:
* Compound of five cubes There are 3 uniform compounds of cubes:
* Compound of six cubes with rotational freedom, UC7
* Compound of three cubes, UC8 There is

Compound of two great icosahedra

The compound of two great icosahedra is a uniform polyhedron compound. It's composed of 2 great icosahedra, in the same arrangement as in the compound of 2 icosahedra. The triangles in this compound d

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.

Compound of six cubes

A compound of six cubes has two forms. One form is a symmetric arrangement of six cubes, considered as square prisms. It is a special case of the compound of six cubes with rotational freedom. Another

Compound of five cuboctahedra

In geometry, this uniform polyhedron compound is a composition of 5 cuboctahedra. It has icosahedral symmetry Ih.

Uniform polyhedron compound

In geometry, a uniform polyhedron compound is a polyhedral compound whose constituents are identical (although possibly enantiomorphous) uniform polyhedra, in an arrangement that is also uniform, i.e.

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.

Compound of two great inverted snub icosidodecahedra

This uniform polyhedron compound is a composition of the 2 enantiomers of the great inverted snub icosidodecahedron.

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.

Compound of three cubes

In geometry, the compound of three cubes is a uniform polyhedron compound formed from three cubes arranged with octahedral symmetry. It has been depicted in works by Max Brückner and M.C. Escher.

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. It results from composing the t

Compound of five octahedra

The compound of five octahedra is one of the five regular polyhedron compounds. This polyhedron can be seen as either a polyhedral stellation or a compound. This compound was first described by Edmund

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.

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.

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. The triangles in this compound decompose into two orbits under acti

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.

Compound of twenty octahedra

The compound of twenty octahedra is a uniform polyhedron compound. It's composed of a symmetric arrangement of 20 octahedra (considered as triangular antiprisms). It is a special case of the compound

Compound of two icosahedra

This uniform polyhedron compound is a composition of 2 icosahedra. It has octahedral symmetry Oh. As a holosnub, it is represented by Schläfli symbol β{3,4} and Coxeter diagram . The triangles in this

Compound of twelve pentagonal antiprisms with rotational freedom

This uniform polyhedron compound is a symmetric arrangement of 12 pentagonal antiprisms. It can be constructed by inscribing one pair of pentagonal antiprisms within an icosahedron, in each of the six

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.

Compound of twenty tetrahemihexahedra

This uniform polyhedron compound is a symmetric arrangement of 20 tetrahemihexahedra. It is chiral with icosahedral symmetry (I). John Skilling notes, in his enumeration of uniform compounds of unifor

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. It is one of only five polyhedral compounds (along with

Compound of two tetrahedra

In geometry, a compound of two tetrahedra is constructed by two overlapping tetrahedra, usually implied as regular tetrahedra.

Compound of four octahedra with rotational freedom

The compound of four octahedra with rotational freedom is a uniform polyhedron compound. It consists in a symmetric arrangement of 4 octahedra, considered as triangular antiprisms. It can be construct

Compound of tesseract and 16-cell

In 4-dimensional geometry, the tesseract 16-cell compound is a polytope compound composed of a regular tesseract and its dual, the regular 16-cell. Its convex hull is the regular 24-cell, which is sel

Compound of two snub dodecadodecahedra

This uniform polyhedron compound is a composition of the 2 enantiomers of the snub dodecadodecahedron.

Compound of two snub cubes

This uniform polyhedron compound is a composition of the 2 enantiomers of the snub cube. As a holosnub, it is represented by Schläfli symbol βr{4,3} and Coxeter diagram . The vertex arrangement of thi

Compound of five tetrahedra

The compound of five tetrahedra is one of the five regular polyhedral compounds. This compound polyhedron is also a stellation of the regular icosahedron. It was first described by Edmund Hess in 1876

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.

Compound of ten tetrahedra

The compound of ten tetrahedra is one of the five regular polyhedral compounds. This polyhedron can be seen as either a stellation of the icosahedron or a compound. This compound was first described b

Compound of ten octahedra

The compounds of ten octahedra UC15 and UC16 are two uniform polyhedron compounds. They are composed of a symmetric arrangement of 10 octahedra, considered as triangular antiprisms, aligned with the a

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.

Compound of cube and octahedron

The compound of cube and octahedron is a polyhedron which can be seen as either a polyhedral stellation or a compound.

Prismatic compound of antiprisms

In geometry, a prismatic compound of antiprism is a category of uniform polyhedron compound. Each member of this infinite family of uniform polyhedron compounds is a symmetric arrangement of antiprism

Compound of two great retrosnub icosidodecahedra

The compound of two great retrosnub icosidodecahedra is a uniform polyhedron compound. It's composed of the 2 enantiomers of the great retrosnub icosidodecahedron.

Compound of small stellated dodecahedron and great dodecahedron

The compound of small stellated dodecahedron and great dodecahedron is a polyhedron compound where the great dodecahedron is internal to its dual, the small stellated dodecahedron. This can be seen as

Compound of dodecahedron and icosahedron

In geometry, this polyhedron can be seen as either a polyhedral stellation or a compound.

Small complex icosidodecahedron

In geometry, the small complex icosidodecahedron is a degenerate uniform star polyhedron. Its edges are doubled, making it degenerate. The star has 32 faces (20 triangles and 12 pentagons), 60 (double

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.

Compound of four tetrahedra

In geometry, a compound of four tetrahedra can be constructed by four tetrahedra in a number of different symmetry positions. One compound can be constructed rotating a tetrahedron by 45 degree turns

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