Pentagrammic crossed-antiprism
Encyclopedia
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 pentagram
s.
It differs from the pentagrammic antiprism
by having opposite orientations on the two pentagrams.
This polyhedron is identified with the indexed name U80 as a uniform polyhedron
.
The pentagrammic crossed-antiprism may be inscribed within an icosahedron
, and has ten triangular faces in common with the great icosahedron. It has the same vertex arrangement
as the pentagonal antiprism
. In fact, it may be considered as a parabidiminished great icosahedron.
Geometry
Geometry arose as the field of knowledge dealing with spatial relationships. Geometry was one of the two fields of pre-modern mathematics, the other being the study of numbers ....
, 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 pentagram
Pentagram
A pentagram is the shape of a five-pointed star drawn with five straight strokes...
s.
It differs from the pentagrammic antiprism
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.This polyhedron is identified with the indexed name U79 as a uniform polyhedron....
by having opposite orientations on the two pentagrams.
This polyhedron is identified with the indexed name U80 as a uniform polyhedron
Uniform polyhedron
A uniform polyhedron is a polyhedron which has regular polygons as faces and is vertex-transitive...
.
 An alternative representation with hollow pentagrams. |
The pentagrammic crossed-antiprism may be inscribed within an icosahedron
Icosahedron
In geometry, an icosahedron is a regular polyhedron with 20 identical equilateral triangular faces, 30 edges and 12 vertices. It is one of the five Platonic solids....
, and has ten triangular faces in common with the great icosahedron. It has the same vertex arrangement
Vertex 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....
as the pentagonal antiprism
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. It consists of two pentagons joined to each other by a ring of 10 triangles for a total of 12 faces...
. In fact, it may be considered as a parabidiminished great icosahedron.
 Pentagrammic crossed-antiprism |
Great icosahedron coloured with D5d symmetry |
External links
- http://www.mathconsult.ch/showroom/unipoly/80.html
- http://mathworld.wolfram.com/PentagrammicCrossedAntiprism.html
- http://bulatov.org/polyhedra/uniform/u05.html
- http://www.math.technion.ac.il/~rl/kaleido/data/05.html