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User:Tomruen/4D cupola

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Cupola (geometry) as regular or quasiregular base and related cells in parallel in parallel.

Polyhedral cupolae
Name Tetrahedral cupola Cubic cupola Octahedral cupola Dodecahedral cupola Icosahedral cupola
(Hyperbolic)
Hexagonal tiling cupola
(Hyperbolic)
Schläfli symbol {3,3} ∨ rr{3,3} {4,3} ∨ rr{4,3} {3,4} ∨ rr{3,4} {5,3} ∨ rr{5,3} {3,5} ∨ rr{3,5} {6,3} ∨ rr{6,3}
Segmentochora
index[1]
K4.23 K4.71 K4.107 K4.152
circumradius 1 sqrt((3+sqrt(2))/2)
= 1.485634
sqrt(2+sqrt(2))
= 1.847759
3+sqrt(5)
= 5.236068
Image
Cap cells
Vertices 16 32 30 80 72
Edges 42 84 84 210 210
Faces 42 24 {3} + 18 {4} 80 32 {3} + 48 {4} 82 40 {3} + 42 {4} 194 80 {3} + 90 {4} + 24 {5} 202 100 {3} + 90 {4} + 12 {5} {3} + ∞ {4} + ∞ {6}
Cells 16 1 tetrahedron
4 triangular prisms
6 triangular prisms
4 triangular pyramids
1 cuboctahedron
28  1 cube
 6 square prisms
12 triangular prisms
 8 triangular pyramids
 1 rhombicuboctahedron
28  1 octahedron
 8 triangular prisms
12 triangular prisms
 6 square pyramids
1 rhombicuboctahedron
64  1 dodecahedron
12 pentagonal prisms
30 triangular prisms
20 triangular pyramids
 1 rhombicosidodecahedron
64  1 icosahedron
20 triangular prisms
30 triangular prisms
12 pentagonal pyramids
 1 rhombicosidodecahedron
1 hexagonal tiling
∞ hexagonal prisms
∞ triangular prisms
∞ triangular pyramids
1 rhombitrihexagonal tiling
Related
uniform
polychora
runcinated 5-cell
runcinated tesseract
runcinated 24-cell
runcinated 120-cell
runcinated icosahedral honeycomb
runcinated hexagonal tiling honeycomb
Polyhedral recti-cupolae
Schläfli symbol {3,3} ∨ r{3,3}
Rectified 5-cell
{3,4} ∨ r{3,4} {4,3} ∨ r{4,3} r{4,3} ∨ rr{4,3} {5,3} ∨ r{5,3} {3,5} ∨ r{3,5} r{5,3} ∨ rr{5,3}
Symmetry [1,3,3] [1,4,3] [1,5,3]
Images
Cap cells
Segmentochora
index
K4.5 K4.29 K4.35 K4.61 K4.77 K4.137 K4.131
circumradius sqrt(3/5) = 0.774597 1 sqrt((16+6*sqrt(2))/23)
= 1.031784
(1+sqrt(8))/sqrt(7)
= 1.447009
(1+sqrt(5))/2
= 1.618034
sqrt(5+2*sqrt(5))
= 3.077684
sqrt(5+2*sqrt(5))
= 3.077684
Vertices 4+6 6+12 8+12 12+24 20+30 12+30 30+60
Edges 30 60 60 120 150 150 300
Faces 30 30 {3} 58 52 {3}, 6 {4} 56 44 {3}, 12 {4} 112 88 {3}, 24 {4} 134 110 {3}, 24 {5} 142 130 {3}, 12 {5} 274 220 {3}, 30 {4}, 24 {5}
Cells 10 1 tetrahedron
4 tetrahedral
4 octahedra
1 octahedron
16 1 octahedron
8 octahedra
6 square pyramids
1 cuboctahedron
16 1 cube
8 tetrahedra
6 square antiprisms
1 cuboctahedron
28 1 cuboctahedron
8 octahedra
12 square pyramids
6 square antiprisms
1 rhombicuboctahedron
34 1 dodecahedron
20 tetrahedra
12 pentagonal antiprisms
1 icosidodecahedron
34 1 icosahedron
20 octahedra
12 pentagonal pyramids
1 icosidodecahedron
64 1 icosidodecahedron
20 octahedra
12 pentagonal antiprisms
30 square pyramids
1 rhombicosidodecahedron
Related
uniform
polychora
Rectified 5-cell half
24-cell
Rectified 600-cell
Polyhedral antiprisms
Schläfli symbol {3,3} ∨ 2r{3,3} t{3,3} ∨ 2t{3,3} {4,3} ∨ 2r{4,3} t{3,4} ∨ 2t{3,4} {5,3} ∨ 2r{5,3} t{5,3} ∨ 2t{5,3}
Symmetry [2+,4,3] [1,4,3] [1,5,3]
Image
Cap cells
Segmentochora
index
K4.2 K4.55 K4.15 K4.98 K4.78 K4.151
Vertices 4+4 12+12 6+8 24+24 12+20 60+60
Edges 24 60 48 120 120 300
Faces 32 32 {3} 52 52 {3} 62 56 {3}, 6 {4} 100 88 {3}, 12 {4} 152 140 {3}, 12 {5} 244 220 {3}, 24 {5}
Cells 16 1 tetrahedron
4 tetrahedra
6 tetrahedra
4 tetrahedra
1 tetrahedron
16 1 truncated tetrahedron
4 trigonal cupola
6 tetrahedra
4 trigonal cupola
1 truncated tetrahedron
28 1 octahedron
8 tetrahedra
12 tetrahedra
6 square pyramids
1 cube
28 1 truncated octahedron
8 trigonal cupolae
12 tetrahedral
6 square cupolae
1 truncated cube
64 1 icosahedron
20 tetrahedra
30 tetrahedra
12 pentagonal pyramids
1 dodecahedron
64 1 truncated icosahedron
20 trigonal cupolae
30 tetrahedra
12 pentagonal cupolae
1 truncated dodecahedron
Related
uniform
polychora
16-cell
Tetrahedral antiprism
s{2,4,3}
Rectified tesseract
  1. ^ Cite error: The named reference Segmentochora was invoked but never defined (see the help page).