View source for Prismatic uniform 4-polytope

{{short description|Type of uniform 4-polytope in four-dimensional geography}}
[[File:4-4 duoprism.png|thumb|A '''cubic prism''', {4,3}×{}, is a lower symmetry construction of the regular [[Tesseract|tesseract]], {4,3,3}, as a prism of two parallel [[Cube|cube]]s, as seen in this [[Schlegel diagram|Schlegel diagram]]]]
In four-dimensional [[Geometry|geometry]], a '''prismatic uniform 4-polytope''' is a uniform 4-polytope with a nonconnected Coxeter diagram symmetry group.{{fact|date=December 2012|reason=Has this term ever been used in a reliable source?}} These figures are analogous to the set of [[Prism (geometry)|prism]]s and [[Antiprism|antiprism]] uniform polyhedra, but add a third category called [[Duoprism|duoprism]]s, constructed as a product of two regular polygons.

The prismatic uniform 4-polytopes consist of two infinite families:
* Polyhedral prisms: products of a line segment and a uniform polyhedron.  This family is infinite because it includes prisms built on 3-dimensional prisms and [[Antiprism|antiprism]]s.
* [[Duoprism]]s: product of two regular polygons.

== Convex polyhedral prisms ==
The most obvious family of prismatic 4-polytopes is the ''polyhedral prisms,'' i.e. products of a polyhedron with a [[Line segment|line segment]].  The cells of such a 4-polytope are two identical uniform polyhedra lying in parallel [[Hyperplane|hyperplane]]s (the ''base'' cells) and a layer of prisms joining them (the ''lateral'' cells).  This family includes prisms for the 75 nonprismatic [[Uniform polyhedron|uniform polyhedra]] (of which 18 are convex; one of these, the cube-prism, is listed above as the ''tesseract'').{{citation needed|date=January 2011}}

There are '''18 convex polyhedral prisms''' created from 5 [[Platonic solid]]s and 13 [[Archimedean solid]]s as well as for the infinite families of three-dimensional [[Prism (geometry)|prism]]s and [[Antiprism|antiprism]]s.{{citation needed|date=January 2011}}  The symmetry number of a polyhedral prism is twice that of the base polyhedron.

== Tetrahedral prisms: A<sub>3</sub> × A<sub>1</sub> ==
{| class="wikitable"
!rowspan=2|#
!rowspan=2| Johnson Name (Bowers style acronym)
!rowspan=2| [[Schlegel diagram|Picture]]
!rowspan=2|Coxeter diagram<BR>and [[Schläfli symbol#Extended for uniform polychora and 3-space honeycombs|Schläfli]]<BR>symbols
!rowspan=2 colspan=3|Cells by type
!colspan=4|Element counts
|-
! Cells
! Faces
! Edges
! Vertices
|-
!48
|align=center|[[Tetrahedral prism]] (tepe)
|[[File:Tetrahedral prism.png|50px]]
|align=center|{{CDD|node_1|3|node|3|node|2|node_1}}<BR>{3,3}×{}
|2 [[File:Tetrahedron.png|20px]]<BR>[[Tetrahedron|3.3.3]]
|4 [[File:Triangular prism.png|20px]]<BR>[[Triangular prism|3.4.4]]
|
|6
|8 {3}<BR>6 {4}
|16
|8
|-
!49
|align=center|[[Truncated tetrahedral prism]] (tuttip)
|[[File:Truncated tetrahedral prism.png|50px]]
|align=center|{{CDD|node_1|3|node_1|3|node|2|node_1}}<BR>t{3,3}×{}
|2 [[File:Truncated tetrahedron.png|20px]]<BR>[[Truncated tetrahedron|3.6.6]]
|4 [[File:Triangular prism.png|20px]]<BR>[[Triangular prism|3.4.4]]
|4 [[File:Hexagonal prism.png|20px]]<BR>[[Hexagonal prism|4.4.6]]
|10
|8 {3}<BR>18 {4}<BR>8 {6}
|48
|24
|-
![51]
|align=center|''Rectified tetrahedral prism''<BR>(Same as [[Octahedral prism|octahedral prism]]) (ope)
|[[File:Octahedral prism.png|50px]]
|align=center|{{CDD|node|3|node_1|3|node|2|node_1}}<BR>r{3,3}×{}
|2 [[File:Octahedron.png|20px]]<BR>[[Octahedron|3.3.3.3]]
|4 [[File:Triangular prism.png|20px]]<BR>[[Triangular prism|3.4.4]]
|
|6
|16 {3}<BR>12 {4}
|30
|12
|-
![50]
|align=center|''Cantellated tetrahedral prism''<BR>(Same as [[Cuboctahedral prism|cuboctahedral prism]]) (cope)
| [[File:Cuboctahedral prism.png|50px]]
|align=center|{{CDD|node_1|3|node|3|node_1|2|node_1}}<BR>rr{3,3}×{}
|2 [[File:Cuboctahedron.png|20px]]<BR>[[Cuboctahedron|3.4.3.4]]
|8 [[File:Triangular prism.png|20px]]<BR>[[Triangular prism|3.4.4]]
|6 [[File:Hexahedron.png|20px]]<BR>[[Cube|4.4.4]]
|16
|16 {3}<BR>36 {4}
|60
|24
|-
![54]
|align=center|''Cantitruncated tetrahedral prism''<BR>(Same as [[Truncated octahedral prism|truncated octahedral prism]]) (tope)
|[[File:Truncated octahedral prism.png|50px]]
|align=center|{{CDD|node_1|3|node_1|3|node_1|2|node_1}}<BR>tr{3,3}×{}
|2 [[File:Truncated octahedron.png|20px]]<BR>[[Truncated octahedron|4.6.6]] 
|8 [[File:Hexagonal prism.png|20px]]<BR>[[Hexagonal prism|3.4.4]]
|6 [[File:Hexahedron.png|20px]]<BR>[[Cube|4.4.4]]
|16
|48 {4}<BR>16 {6}
|96
|48
|-
![59]
|align=center|''Snub tetrahedral prism''<BR>(Same as [[Icosahedral prism|icosahedral prism]]) (ipe)
|[[File:Icosahedral prism.png|50px]]
|align=center|{{CDD|node_h|3|node_h|3|node_h|2|node_1}}<BR>sr{3,3}×{}
|2 [[File:Icosahedron.png|20px]]<BR>[[Icosahedron|3.3.3.3.3]]
|20 [[File:Triangular prism.png|20px]]<BR>[[Triangular prism|3.4.4]]
|
|22
|40 {3}<BR>30 {4}
|72
|24
|}

== Octahedral prisms: BC<sub>3</sub> × A<sub>1</sub> ==
{| class="wikitable"
!rowspan=2| #
!rowspan=2| Johnson Name (Bowers style acronym)
!rowspan=2| [[Schlegel diagram|Picture]]
!rowspan=2|Coxeter diagram<BR>and [[Schläfli symbol#Extended for uniform polychora and 3-space honeycombs|Schläfli]]<BR>symbols
!rowspan=2 colspan=4|Cells by type
!colspan=4|Element counts
|-
! Cells
! Faces
! Edges
! Vertices
|-
![10]
|align=center|''Cubic prism''<BR>(Same as '''[[Tesseract|tesseract]]''')<BR>(Same as ''4-4 duoprism'') (tes)
|[[File:Schlegel wireframe 8-cell.png|50px]]
|align=center|{{CDD|node_1|4|node|3|node|2|node_1}}<BR>{4,3}×{}
|2 [[File:Hexahedron.png|20px]]<BR>[[Cube|4.4.4]]
|6 [[File:Hexahedron.png|20px]]<BR>[[Cube|4.4.4]]
|
|
|8
|24 {4}
|32
|16
|-
!50
|align=center|[[Cuboctahedral prism]]<BR>(Same as ''cantellated tetrahedral prism'') (cope)
|[[File:Cuboctahedral prism.png|50px]]
|align=center|{{CDD|node|4|node_1|3|node|2|node_1}}<BR>r{4,3}×{}
| 2 [[File:Cuboctahedron.png|20px]]<BR>[[Cuboctahedron|3.4.3.4]] 
| 8 [[File:Triangular prism.png|20px]]<BR>[[Triangular prism|3.4.4]]
| 6 [[File:Hexahedron.png|20px]]<BR>[[Cube|4.4.4]]
|
| 16
| 16 {3}<BR>36 {4}
| 60
| 24
|-
!51
|align=center|[[Octahedral prism]]<BR>(Same as ''rectified tetrahedral prism'')<BR>(Same as ''triangular antiprismatic prism'') (ope)
|[[File:Octahedral prism.png|50px]]
|align=center|{{CDD|node|4|node|3|node_1|2|node_1}}<BR>{3,4}×{}
|2 [[File:Octahedron.png|20px]]<BR>[[Octahedron|3.3.3.3]]
|8 [[File:Triangular prism.png|20px]]<BR>[[Triangular prism|3.4.4]]
|
|
|10
|16 {3}<BR>12 {4}
|30
|12
|-
!52
|align=center|[[Rhombicuboctahedral prism]] (sircope)
|[[File:Rhombicuboctahedral prism.png|50px]]
|align=center|{{CDD|node_1|4|node|3|node_1|2|node_1}}<BR>rr{4,3}×{}
| 2 [[File:Small rhombicuboctahedron.png|20px]]<BR>[[Rhombicuboctahedron|3.4.4.4]] 
| 8 [[File:Triangular prism.png|20px]]<BR>[[Triangular prism|3.4.4]]
| 18 [[File:Hexahedron.png|20px]]<BR>[[Cube|4.4.4]]
|
| 28
| 16 {3}<BR>84 {4}
| 120
| 96
|-
!53
|align=center|[[Truncated cubic prism]] (ticcup)
|[[File:Truncated cubic prism.png|50px]]
|align=center|{{CDD|node_1|4|node_1|3|node|2|node_1}}<BR>t{4,3}×{}
| 2 [[File:Truncated hexahedron.png|20px]]<BR>[[Truncated cube|3.8.8]]
| 8 [[File:Triangular prism.png|20px]]<BR>[[Triangular prism|3.4.4]]
| 6 [[File:Octagonal prism.png|20px]]<BR>[[Octagonal prism|4.4.8]]
|
| 16
| 16 {3}<BR>36 {4}<BR>12 {8}
| 96
| 48
|-
!54
|align=center|[[Truncated octahedral prism]]<BR>(Same as ''cantitruncated tetrahedral prism'') (tope)
|[[File:Truncated octahedral prism.png|50px]]
|align=center|{{CDD|node|4|node_1|3|node_1|2|node_1}}<BR>t{3,4}×{}
| 2 [[File:Truncated octahedron.png|20px]]<BR>[[Truncated octahedron|4.6.6]]
| 6 [[File:Hexahedron.png|20px]]<BR>[[Cube|4.4.4]]
| 8 [[File:Hexagonal prism.png|20px]]<BR>[[Hexagonal prism|4.4.6]]
|
| 16
| 48 {4}<BR>16 {6}
| 96
| 48
|-
!55
|align=center|[[Truncated cuboctahedral prism]] (gircope)
|[[File:Truncated cuboctahedral prism.png|50px]]
|align=center|{{CDD|node_1|4|node_1|3|node_1|2|node_1}}<BR>tr{4,3}×{}
| 2 [[File:Great rhombicuboctahedron.png|20px]]<BR>[[Truncated cuboctahedron|4.6.8]]
| 12 [[File:Hexahedron.png|20px]]<BR>[[Cube|4.4.4]]
| 8 [[File:Hexagonal prism.png|20px]]<BR>[[Hexagonal prism|4.4.6]]
| 6 [[File:Octagonal prism.png|20px]]<BR>[[Octagonal prism|4.4.8]]
| 28
| 96 {4}<BR>16 {6}<BR>12 {8}
| 192
| 96
|-
!56
|align=center|[[Snub cubic prism]] (sniccup)
|[[File:Snub cubic prism.png|50px]]
|align=center|{{CDD|node_h|4|node_h|3|node_h|2|node_1}}<BR>sr{4,3}×{}
| 2 [[File:Snub hexahedron.png|20px]]<BR>[[Snub cube|3.3.3.3.4]]
| 32 [[File:Triangular prism.png|20px]]<BR>[[Triangular prism|3.4.4]]
| 6 [[File:Hexahedron.png|20px]]<BR>[[Cube|4.4.4]]
|
| 40
| 64 {3}<BR>72 {4}
| 144
| 48
|}

== Icosahedral prisms: H<sub>3</sub> × A<sub>1</sub> ==

{| class="wikitable"
!rowspan=2|#
!rowspan=2| Johnson Name (Bowers style acronym)
!rowspan=2| [[Schlegel diagram|Picture]]
!rowspan=2|Coxeter diagram<BR>and [[Schläfli symbol#Extended for uniform polychora and 3-space honeycombs|Schläfli]]<BR>symbols
!rowspan=2 colspan=4|Cells by type
!colspan=4|Element counts
|-
! Cells
! Faces
! Edges
! Vertices
|-
!57
|align=center|[[Dodecahedral prism]] (dope)
|[[File:Dodecahedral prism.png|50px]]
|align=center|{{CDD|node_1|5|node|3|node|2|node_1}}<BR>{5,3}×{}
| 2 [[File:Dodecahedron.png|20px]]<BR>[[Dodecahedron|5.5.5]]
|12 [[File:Pentagonal prism.png|20px]]<BR>[[Pentagonal prism|4.4.5]]
|
|
| 14
| 30 {4}<BR>24 {5}
| 80
| 40
|-
!58
|align=center|[[Icosidodecahedral prism]] (iddip)
|[[File:Icosidodecahedral prism.png|50px]]
|align=center|{{CDD|node|5|node_1|3|node|2|node_1}}<BR>r{5,3}×{}
|2 [[File:Icosidodecahedron.png|20px]]<BR>[[Icosidodecahedron|3.5.3.5]]
|20 [[File:Triangular prism.png|20px]]<BR>[[Triangular prism|3.4.4]]
|12 [[File:Pentagonal prism.png|20px]]<BR>[[Pentagonal prism|4.4.5]]
|
| 34
| 40 {3}<BR>60 {4}<BR>24 {5}
| 150
| 60
|-
!59
|align=center|[[Icosahedral prism]]<BR>(same as ''snub tetrahedral prism'') (ipe)
|[[File:Icosahedral prism.png|50px]]
|align=center|{{CDD|node|5|node|3|node_1|2|node_1}}<BR>{3,5}×{}
|2 [[File:Icosahedron.png|20px]]<BR>[[Icosahedron|3.3.3.3.3]] 
|20 [[File:Triangular prism.png|20px]]<BR>[[Triangular prism|3.4.4]]
|
|
| 22
| 40 {3}<BR>30 {4}
| 72
| 24
|-
!60
|align=center|[[Truncated dodecahedral prism]] (tiddip)
|[[File:Truncated dodecahedral prism.png|50px]]
|align=center|{{CDD|node_1|5|node_1|3|node|2|node_1}}<BR>t{5,3}×{}
|2 [[File:Truncated dodecahedron.png|20px]]<BR>[[Truncated dodecahedron|3.10.10]]
|20 [[File:Triangular prism.png|20px]]<BR>[[Triangular prism|3.4.4]]
|12 [[File:Decagonal prism.png|20px]]<BR>[[Decagonal prism|4.4.5]]
| 
| 34
| 40 {3}<BR>90 {4}<BR>24 {10}
| 240
| 120
|-
!61
|align=center|[[Rhombicosidodecahedral prism]] (sriddip)
|[[File:Rhombicosidodecahedral prism.png|50px]]
|align=center|{{CDD|node_1|5|node|3|node_1|2|node_1}}<BR>rr{5,3}×{}
|2 [[File:Small rhombicosidodecahedron.png|20px]]<BR>[[Rhombicosidodecahedron|3.4.5.4]]
|20 [[File:Triangular prism.png|20px]]<BR>[[Triangular prism|3.4.4]]
|30 [[File:Hexahedron.png|20px]]<BR>[[Cube|4.4.4]]
|12 [[File:Pentagonal prism.png|20px]]<BR>[[Pentagonal prism|4.4.5]]
| 64
| 40 {3}<BR>180 {4}<BR>24 {5}
| 300
| 120
|-
!62
|align=center|[[Truncated icosahedral prism]] (tipe)
|[[File:Truncated icosahedral prism.png|50px]]
|align=center|{{CDD|node|5|node_1|3|node_1|2|node_1}}<BR>t{3,5}×{}
|2 [[File:Truncated icosahedron.png|20px]]<BR>[[Truncated icosahedron|5.6.6]] 
|12 [[File:Pentagonal prism.png|20px]]<BR>[[Pentagonal prism|4.4.5]]
|20 [[File:Hexagonal prism.png|20px]]<BR>[[Hexagonal prism|4.4.6]]
|
| 34
| 90 {4}<BR>24 {5}<BR>40 {6}
| 240
| 120
|-
!63
|align=center|[[Truncated icosidodecahedral prism]] (griddip)
|[[File:Truncated icosidodecahedral prism.png|50px]]
|align=center|{{CDD|node_1|5|node_1|3|node_1|2|node_1}}<BR>tr{5,3}×{}
|2 [[File:Great rhombicosidodecahedron.png|20px]]<BR>[[Truncated icosidodecahedron|4.6.4.10]] 
|30 [[File:Hexahedron.png|20px]]<BR>[[Cube|4.4.4]]
|20 [[File:Hexagonal prism.png|20px]]<BR>[[Hexagonal prism|4.4.6]]
|12 [[File:Decagonal prism.png|20px]]<BR>[[Decagonal prism|4.4.10]]
| 64
| 240 {4}<BR>40 {6}<BR>24 {5}
| 480
| 240
|-
!64
|align=center|[[Snub dodecahedral prism]] (sniddip)
|[[File:Snub dodecahedral prism.png|50px]]
|align=center|{{CDD|node_h|5|node_h|3|node_h|2|node_1}}<BR>sr{5,3}×{}
|2 [[File:Snub dodecahedron ccw.png|20px]]<BR>[[Snub dodecahedron|3.3.3.3.5]]
|80 [[File:Triangular prism.png|20px]]<BR>[[Triangular prism|3.4.4]]
|12 [[File:Pentagonal prism.png|20px]]<BR>[[Pentagonal prism|4.4.5]]
|
| 94
| 240 {4}<BR>40 {6}<BR>24 {10}
| 360
| 120
|}

== Duoprisms: [p] × [q] ==
{| class="wikitable" align=right
|+ Set of uniform p,q duoprisms
|- align=center
|[[File:3-3 duoprism.png|50px]]<BR>3-3
|[[File:3-4 duoprism.png|50px]]<BR>3-4
|[[File:3-5 duoprism.png|50px]]<BR>3-5
|[[File:3-6 duoprism.png|50px]]<BR>3-6
|[[File:3-7 duoprism.png|50px]]<BR>3-7
|[[File:3-8 duoprism.png|50px]]<BR>3-8
|- align=center
|[[File:4-3 duoprism.png|50px]]<BR>4-3
|[[File:4-4 duoprism.png|50px]]<BR>4-4
|[[File:4-5 duoprism.png|50px]]<BR>4-5
|[[File:4-6 duoprism.png|50px]]<BR>4-6
|[[File:4-7 duoprism.png|50px]]<BR>4-7
|[[File:4-8 duoprism.png|50px]]<BR>4-8
|- align=center
|[[File:5-3 duoprism.png|50px]]<BR>5-3
|[[File:5-4 duoprism.png|50px]]<BR>5-4
|[[File:5-5 duoprism.png|50px]]<BR>5-5
|[[File:5-6 duoprism.png|50px]]<BR>5-6
|[[File:5-7 duoprism.png|50px]]<BR>5-7
|[[File:5-8 duoprism.png|50px]]<BR>5-8
|- align=center
|[[File:6-3 duoprism.png|50px]]<BR>6-3
|[[File:6-4 duoprism.png|50px]]<BR>6-4
|[[File:6-5 duoprism.png|50px]]<BR>6-5
|[[File:6-6 duoprism.png|50px]]<BR>6-6
|[[File:6-7 duoprism.png|50px]]<BR>6-7
|[[File:6-8 duoprism.png|50px]]<BR>6-8
|- align=center
|[[File:7-3 duoprism.png|50px]]<BR>7-3
|[[File:7-4 duoprism.png|50px]]<BR>7-4
|[[File:7-5 duoprism.png|50px]]<BR>7-5
|[[File:7-6 duoprism.png|50px]]<BR>7-6
|[[File:7-7 duoprism.png|50px]]<BR>7-7
|[[File:7-8 duoprism.png|50px]]<BR>7-8
|- align=center
|[[File:8-3 duoprism.png|50px]]<BR>8-3
|[[File:8-4 duoprism.png|50px]]<BR>8-4
|[[File:8-5 duoprism.png|50px]]<BR>8-5
|[[File:8-6 duoprism.png|50px]]<BR>8-6
|[[File:8-7 duoprism.png|50px]]<BR>8-7
|[[File:8-8 duoprism.png|50px]]<BR>8-8
|}

The second is the infinite family of [[Duoprism|uniform duoprisms]], products of two [[Regular polygon|regular polygon]]s. 

Their Coxeter diagram is of the form {{CDD|node_1|p|node|2|node_1|q|node}}

This family overlaps with the first: when one of the two "factor" polygons is a square, the product is equivalent to a hyperprism whose base is a three-dimensional prism.  The symmetry number of a duoprism whose factors are a ''p''-gon and a ''q''-gon (a "''p,q''-duoprism") is 4''pq'' if ''p''≠''q''; if the factors are both ''p''-gons, the symmetry number is 8''p''<sup>2</sup>. The tesseract can also be considered a 4,4-duoprism.

The elements of a ''p,q''-duoprism (''p'' ≥ 3, ''q'' ≥ 3) are:
* Cells: '''p''' ''q''-gonal prisms, '''q''' ''p''-gonal prisms
* Faces: '''pq''' squares, '''p''' ''q''-gons, '''q''' ''p''-gons
* Edges: '''2pq'''
* Vertices: '''pq'''

There is no uniform analogue in four dimensions to the infinite family of three-dimensional [[Antiprism|antiprism]]s with the exception of the [[Great duoantiprism|great duoantiprism]].

Infinite set of '''p-q duoprism''' - {{CDD|node_1|p|node|2|node_1|q|node}} - '''p''' ''q''-gonal prisms, '''q''' ''p''-gonal prisms:
* '''3-3 duoprism''' - {{CDD|node_1|3|node|2|node_1|3|node}} - '''6''' triangular prisms
* '''3-4 duoprism''' - {{CDD|node_1|3|node|2|node_1|4|node}} - '''3''' cubes, '''4''' triangular prisms
* '''4-4 duoprism''' - {{CDD|node_1|4|node|2|node_1|4|node}} - '''8''' cubes (same as '''tesseract''')
* '''3-5 duoprism''' - {{CDD|node_1|3|node|2|node_1|5|node}} - '''3''' pentagonal prisms, '''5''' triangular prisms
* '''4-5 duoprism''' - {{CDD|node_1|4|node|2|node_1|5|node}} - '''4''' pentagonal prisms, '''5''' cubes
* '''5-5 duoprism''' - {{CDD|node_1|5|node|2|node_1|5|node}} - '''10''' pentagonal prisms
* '''3-6 duoprism''' - {{CDD|node_1|3|node|2|node_1|6|node}} - '''3''' hexagonal prisms, '''6''' triangular prisms
* '''4-6 duoprism''' - {{CDD|node_1|4|node|2|node_1|6|node}} - '''4''' hexagonal prisms, '''6''' cubes
* '''5-6 duoprism''' - {{CDD|node_1|5|node|2|node_1|6|node}} - '''5''' hexagonal prisms, '''6''' pentagonal prisms
* '''6-6 duoprism''' - {{CDD|node_1|6|node|2|node_1|6|node}} - '''12''' hexagonal prisms
* ...

== Polygonal prismatic prisms ==

The infinite set of uniform prismatic prisms overlaps with the 4-p duoprisms: (p≥3) - {{CDD|node_1|p|node|2|node_1|2|node_1}} - ''p'' cubes and 4 ''p''-gonal prisms - (All are the same as '''4-p duoprism''')
* ''Triangular prismatic prism'' - {{CDD|node_1|3|node|2|node_1|2|node_1}} - 3 cubes and 4 triangular prisms - (same as '''3-4 duoprism''')
* ''Square prismatic prism'' - {{CDD|node_1|4|node|2|node_1|2|node_1}} - 4 cubes and 4 cubes - (same as '''4-4 duoprism''' and same as '''tesseract''')
* ''Pentagonal prismatic prism'' - {{CDD|node_1|5|node|2|node_1|2|node_1}} - 5 cubes and 4 pentagonal prisms - (same as '''4-5 duoprism''')
* ''Hexagonal prismatic prism'' - {{CDD|node_1|6|node|2|node_1|2|node_1}} - 6 cubes and 4 hexagonal prisms - (same as '''4-6 duoprism''')
* ''Heptagonal prismatic prism'' - {{CDD|node_1|7|node|2|node_1|2|node_1}} - 7 cubes and 4 heptagonal prisms - (same as '''4-7 duoprism''')
* ''Octagonal prismatic prism'' - {{CDD|node_1|8|node|2|node_1|2|node_1}} - 8 cubes and 4 octagonal prisms - (same as '''4-8 duoprism''')
* ...
== Uniform antiprismatic prism ==
The infinite sets of '''[[Uniform antiprismatic prism|uniform antiprismatic prism]]s''' or '''antiduoprisms''' are constructed from two parallel uniform [[Antiprism|antiprism]]s: (p≥3) - {{CDD|node_h|p|node_h|2|node_h|2|node_1}} - 2 ''p''-gonal antiprisms, connected by 2 ''p''-gonal prisms and ''2p'' triangular prisms. 

A ''p-gonal antiprismatic prism'' has ''4p'' triangle, ''4p'' square and ''4'' p-gon faces. It has ''10p'' edges, and ''4p'' vertices.

== References ==
* ''[http://www.wiley.com/WileyCDA/WileyTitle/productCd-0471010030.html Kaleidoscopes: Selected Writings of H.S.M. Coxeter]'', edited by F. Arthur Sherk, Peter McMullen, Anthony C. Thompson, Asia Ivic Weiss, Wiley-Interscience Publication, 1995, {{ISBN|978-0-471-01003-6}}
** (Paper 22) H.S.M. Coxeter, ''Regular and Semi-Regular Polytopes I'', [Math. Zeit. 46 (1940) 380-407, MR 2,10]
** (Paper 23) H.S.M. Coxeter, ''Regular and Semi-Regular Polytopes II'', [Math. Zeit. 188 (1985) 559-591]
** (Paper 24) H.S.M. Coxeter, ''Regular and Semi-Regular Polytopes III'', [Math. Zeit. 200 (1988) 3-45]
* [[Biography:John Horton Conway|J.H. Conway]] and M.J.T. Guy: ''Four-Dimensional Archimedean Polytopes'', Proceedings of the Colloquium on Convexity at Copenhagen, page 38 und 39, 1965
* [[Biography:Norman Johnson (mathematician)|N.W. Johnson]]: ''The Theory of Uniform Polytopes and Honeycombs'', Ph.D. Dissertation, University of Toronto, 1966
*[http://www.polytope.de Four-dimensional Archimedean Polytopes] (German), Marco Möller, 2004 PhD dissertation  
* {{KlitzingPolytopes|polychora.htm|4D|uniform polytopes (polychora)}}

{{Polytopes}}

{{DEFAULTSORT:Prismatic Uniform Polychoron}}
[[Category:4-polytopes]]

{{Sourceattribution|Prismatic uniform 4-polytope}}