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In geometry
Geometry (; ) is, with arithmetic, one of the oldest branches of mathematics. It is concerned with properties of space such as the distance, shape, size, and relative position of figures. A mathematician who works in the field of geometry is c ...
, a truncated icosidodecahedral prism or great rhombicosidodecahedral prism is a convex uniform
A uniform is a variety of clothing worn by members of an organization while participating in that organization's activity. Modern uniforms are most often worn by armed forces and paramilitary organizations such as police, emergency services, se ...
4-polytope
In geometry, a 4-polytope (sometimes also called a polychoron, polycell, or polyhedroid) is a four-dimensional polytope. It is a connected and closed figure, composed of lower-dimensional polytopal elements: vertices, edges, faces (polygons), an ...
(four-dimensional polytope).
It is one of 18 convex uniform polyhedral prisms created by using uniform prism
Prism usually refers to:
* Prism (optics), a transparent optical component with flat surfaces that refract light
* Prism (geometry), a kind of polyhedron
Prism may also refer to:
Science and mathematics
* Prism (geology), a type of sedimentary ...
s to connect pairs of Platonic solid
In geometry, a Platonic solid is a convex, regular polyhedron in three-dimensional Euclidean space. Being a regular polyhedron means that the faces are congruent (identical in shape and size) regular polygons (all angles congruent and all edges c ...
s or Archimedean solid
In geometry, an Archimedean solid is one of the 13 solids first enumerated by Archimedes. They are the convex uniform polyhedra composed of regular polygons meeting in identical vertices, excluding the five Platonic solids (which are composed ...
s in parallel hyperplane
In geometry, a hyperplane is a subspace whose dimension is one less than that of its ''ambient space''. For example, if a space is 3-dimensional then its hyperplanes are the 2-dimensional planes, while if the space is 2-dimensional, its hyper ...
s.
Alternative names
* Truncated icosidodecahedral dyadic prism (Norman W. Johnson) * Griddip (Jonathan Bowers: for great rhombicosidodecahedral prism/hyperprism) * Great rhombicosidodecahedral prism/hyperprismRelated polytopes
A full snub dodecahedral antiprism or omnisnub dodecahedral antiprism can be defined as an alternation of an truncated icosidodecahedral prism, represented by ht0,1,2,3, or , although it cannot be constructed as a uniform 4-polytope. It has 184 cells: 2snub 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.
The snub dodecahedron has 92 faces (the most ...
s connected by 30 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. The tetrahedron is the simplest of all the o ...
s, 12 pentagonal antiprisms, and 20 octahedrons, with 120 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. The tetrahedron is the simplest of all the o ...
s in the alternated gaps. It has 120 vertices, 480 edges, and 544 faces (24 pentagons and 40+480 triangles). It has ,3,2sup>+ symmetry, order 120.
Vertex figure
In geometry, a vertex figure, broadly speaking, is the figure exposed when a corner of a polyhedron or polytope is sliced off.
Definitions
Take some corner or Vertex (geometry), vertex of a polyhedron. Mark a point somewhere along each connect ...
for the omnisnub dodecahedral antiprism
External links
* * 4-polytopes {{Polychora-stub