Uniform antiprismatic prism

Set of uniform antiprismatic prismsTypePrismatic uniform 4-polytopeSchläfli symbols{2,p}×{}Coxeter diagramCells2 p-gonal antiprisms,2 p-gonal prisms and2p triangular prismsFaces4p {3}, 4p {4} and 4 {p}Edges10pVertices4pVertex figureTrapezoidal pyramidSymmetry group[2p,2+,2], order 8p[(p,2)+,2], order 4pPropertiesconvex if the base is convex In 4-dimensional geometry, a uniform antiprismatic prism or antiduoprism is a uniform 4-polytope with two uniform antiprism cells in two parallel 3-space hyperplanes, connected by uniform prisms cells between pairs of faces. The symmetry of a p-gonal antiprismatic prism is [2p,2+,2], order 8p.

A p-gonal antiprismatic prism or p-gonal antiduoprism has 2 p-gonal antiprism, 2 p-gonal prism, and 2p triangular prism cells. It has 4p equilateral triangle, 4p square and 4 regular p-gon faces. It has 10p edges, and 4p vertices.

+ Example 15-gonal antiprismatic prismSchlegel diagramNet

Convex uniform antiprismatic prisms There is an infinite series of convex uniform antiprismatic prisms, starting with the digonal antiprismatic prism is a tetrahedral prism, with two of the tetrahedral cells degenerated into squares. The triangular antiprismatic prism is the first nondegenerate form, which is also an octahedral prism. The remainder are unique uniform 4-polytopes.

Star antiprismatic prisms

There are also star forms following the set of star antiprisms, starting with the pentagram {5/2}: NameCoxeterdiagramCellsImageNet (overlapping in space) Pentagrammic antiprismatic prism5/2 antiduoprism 2 pentagrammic antiprisms2 pentagrammic prisms10 triangular prisms Pentagrammic crossed antiprismatic prism5/3 antiduoprism 2 pentagrammic crossed antiprisms 2 pentagrammic prisms10 triangular prisms...

Square antiprismatic prism Square antiprismatic prismTypePrismatic uniform 4-polytopeSchläfli symbols{2,4}x{}Coxeter-DynkinCells2 (3.3.3.4)8 (3.4.4)2 4.4.4 Faces16 {3}, 20 {4}Edges40Vertices16Vertex figureTrapezoidal pyramidSymmetry group[(4,2)+,2], order 16[8,2+,2], order 32Propertiesconvex A square antiprismatic prism or square antiduoprism is a convex uniform 4-polytope. It is formed as two parallel square antiprisms connected by cubes and triangular prisms. The symmetry of a square antiprismatic prism is [8,2+,2], order 32. It has 16 triangle, 16 square and 4 square faces. It has 40 edges, and 16 vertices.

+ Square antiprismatic prismSchlegel diagramNet

Pentagonal antiprismatic prism

Pentagonal antiprismatic prismTypePrismatic uniform 4-polytopeSchläfli symbols{2,5}x{}Coxeter-DynkinCells2 (3.3.3.5) 10 (3.4.4) 2 (4.4.5) Faces20 {3}, 20 {4}, 4 {5}Edges50Vertices20Vertex figureTrapezoidal pyramidSymmetry group[(5,2)+,2], order 20[10,2+,2], order 40Propertiesconvex A pentagonal antiprismatic prism or pentagonal antiduoprism is a convex uniform 4-polytope. It is formed as two parallel pentagonal antiprisms connected by cubes and triangular prisms. The symmetry of a pentagonal antiprismatic prism is [10,2+,2], order 40. It has 20 triangle, 20 square and 4 pentagonal faces. It has 50 edges, and 20 vertices.

+ Pentagonal antiprismatic prismSchlegel diagramNet

Hexagonal antiprismatic prism

Hexagonal antiprismatic prismTypePrismatic uniform 4-polytopeSchläfli symbols{2,6}x{}Coxeter-DynkinCells2 (3.3.3.6) 12 (3.4.4) 2 (4.4.6) Faces24 {3}, 24 {4}, 4 {6}Edges60Vertices24Vertex figureTrapezoidal pyramidSymmetry group[(2,6)+,2], order 24[12,2+,2], order 48Propertiesconvex

A hexagonal antiprismatic prism or hexagonal antiduoprism is a convex uniform 4-polytope. It is formed as two parallel hexagonal antiprisms connected by cubes and triangular prisms. The symmetry of a hexagonal antiprismatic prism is [12,2+,2], order 48. It has 24 triangle, 24 square and 4 hexagon faces. It has 60 edges, and 24 vertices.

+ Hexagonal antiprismatic prismSchlegel diagramNet

Heptagonal antiprismatic prism

Heptagonal antiprismatic prismTypePrismatic uniform 4-polytopeSchläfli symbols{2,7}×{}Coxeter-DynkinCells2 (3.3.3.7) 14 (3.4.4) 2 (4.4.7) Faces28 {3}, 28 {4}, 4 {7}Edges70Vertices28Vertex figureTrapezoidal pyramidSymmetry group[(7,2)+,2], order 28[14,2+,2], order 56Propertiesconvex

A heptagonal antiprismatic prism or heptagonal antiduoprism is a convex uniform 4-polytope. It is formed as two parallel heptagonal antiprisms connected by cubes and triangular prisms. The symmetry of a heptagonal antiprismatic prism is [14,2+,2], order 56. It has 28 triangle, 28 square and 4 heptagonal faces. It has 70 edges, and 28 vertices.

+ Heptagonal antiprismatic prismSchlegel diagramNet

Octagonal antiprismatic prism Octagonal antiprismatic prismTypePrismatic uniform 4-polytopeSchläfli symbols{2,8}×{}Coxeter-DynkinCells2 (3.3.3.8) 16 (3.4.4) 2 (4.4.8) Faces32 {3}, 32 {4}, 4 {8}Edges80Vertices32Vertex figureTrapezoidal pyramidSymmetry group[(8,2)+,2], order 32[16,2+,2], order 64Propertiesconvex

A octagonal antiprismatic prism or octagonal antiduoprism is a convex uniform 4-polytope (four-dimensional polytope). It is formed as two parallel octagonal antiprisms connected by cubes and triangular prisms. The symmetry of an octagonal antiprismatic prism is [16,2+,2], order 64. It has 32 triangle, 32 square and 4 octagonal faces. It has 80 edges, and 32 vertices.

+ Octagonal antiprismatic prismSchlegel diagramNet

Uniform antiprismatic prism

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