Prismatic compound of prisms
Encyclopedia
| Compound of n p/q-gonal prisms | |
|---|---|
 (n=2, p=5, q=2) |
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| Type | Uniform compound Uniform polyhedron compound A uniform polyhedron compound is a polyhedral compound whose constituents are identical uniform polyhedra, in an arrangement that is also uniform: the symmetry group of the compound acts transitively on the compound's vertices.The uniform polyhedron compounds were first enumerated by John Skilling... |
| Index | UC21 |
| Polyhedra | n p/q-gonal prisms Prismatic uniform polyhedron In geometry, a prismatic uniform polyhedron is a uniform polyhedron with dihedral symmetry. They exist in two infinite families, the uniform prisms and the uniform antiprisms... |
| Faces | 2n {p/q}, np squares Square (geometry) In geometry, a square is a regular quadrilateral. This means that it has four equal sides and four equal angles... |
| Edges | 3np |
| Vertices | 2np |
| Symmetry group Symmetry group The symmetry group of an object is the group of all isometries under which it is invariant with composition as the operation... |
np-fold prismatic Dihedral symmetry in three dimensions This article deals with three infinite sequences of point groups in three dimensions which have a symmetry group that as abstract group is a dihedral group Dihn .See also point groups in two dimensions.Chiral:... (Dnph) |
| Subgroup Subgroup In group theory, 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 *. More precisely, H is a subgroup of G if the restriction of * to H x H is a group operation on H... restricting to one constituent |
p-fold prismatic Dihedral symmetry in three dimensions This article deals with three infinite sequences of point groups in three dimensions which have a symmetry group that as abstract group is a dihedral group Dihn .See also point groups in two dimensions.Chiral:... (Dph) |
Each member of this infinite family of uniform polyhedron compound
Uniform polyhedron compound
A uniform polyhedron compound is a polyhedral compound whose constituents are identical uniform polyhedra, in an arrangement that is also uniform: the symmetry group of the compound acts transitively on the compound's vertices.The uniform polyhedron compounds were first enumerated by John Skilling...
s is a symmetric arrangement of prisms
Prismatic uniform polyhedron
In geometry, a prismatic uniform polyhedron is a uniform polyhedron with dihedral symmetry. They exist in two infinite families, the uniform prisms and the uniform antiprisms...
sharing a common axis of rotational symmetry.
This infinite family can be enumerated as follows:
- For each positive integer n>1 and for each rational number p/q>2 (expressed with p and q coprimeCoprimeIn number theory, a branch of mathematics, two integers a and b are said to be coprime or relatively prime if the only positive integer that evenly divides both of them is 1. This is the same thing as their greatest common divisor being 1...
), there occurs the compound of n p/q-gonal prisms, with symmetry group Dnph.