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The compound of twenty octahedra is a
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. the symmetry group of the compound acts tran ...
. It's composed of a symmetric arrangement of 20 octahedra
In geometry, an octahedron (plural: octahedra, octahedrons) is a polyhedron with eight faces. The term is most commonly used to refer to the regular octahedron, a Platonic solid composed of eight equilateral triangles, four of which meet at ea ...
(considered as triangular antiprisms
In geometry, an antiprism or is a polyhedron composed of two parallel direct copies (not mirror images) of an polygon, connected by an alternating band of triangles. They are represented by the Conway notation .
Antiprisms are a subclass ...
). It is a special case of the compound of 20 octahedra with rotational freedom, in which pairs of octahedral vertices coincide.
Related polyhedra
This compound shares itsedge arrangement
In geometry, a vertex arrangement is a set of points in space described by their relative positions. They can be described by their use in polytopes.
For example, a ''square vertex arrangement'' is understood to mean four points in a plane, equ ...
with the great dirhombicosidodecahedron
In geometry, the great dirhombicosidodecahedron (or great snub disicosidisdodecahedron) is a nonconvex uniform polyhedron, indexed last as . It has 124 faces (40 triangles, 60 squares, and 24 pentagrams), 240 edges, and 60 vertices.
This is ...
, the great disnub dirhombidodecahedron
In geometry, the great disnub dirhombidodecahedron, also called ''Skilling's figure'', is a degenerate uniform star polyhedron.
It was proven in 1970 that there are only 75 uniform polyhedra other than the infinite families of prisms and antipr ...
, and the 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 uniform polyhedra, that this compound of 20 tetra ...
.
It may be constructed as the exclusive or
Exclusive or or exclusive disjunction is a logical operation that is true if and only if its arguments differ (one is true, the other is false).
It is symbolized by the prefix operator J and by the infix operators XOR ( or ), EOR, EXOR, , ...
of the two enantiomorphs of the great snub dodecicosidodecahedron
In geometry, the great snub dodecicosidodecahedron (or great snub dodekicosidodecahedron) is a nonconvex uniform polyhedron, indexed as U64. It has 104 faces (80 triangles and 24 pentagrams), 180 edges, and 60 vertices. It has Coxeter diagram, . ...
.
See also
*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 other. Although appearing earlier in the mathemati ...
*Compound of four octahedra
The compound of four octahedra is a uniform polyhedron compound. It's composed of a symmetric arrangement of 4 octahedron, octahedra, considered as triangular antiprisms. It can be constructed by superimposing four identical octahedra, and then r ...
*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 Hess in 1876. It is unique among the regular ...
* Compound of ten octahedra
References
*. Polyhedral compounds {{polyhedron-stub