β°' is the hemi-di-4n+2-gon.
β° is the hemi-4n+2-hosohedron.
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Α | n ≥ 0, no. of edges is odd |
name | Schläfli formula | Vertices, Faces, Edges | mV,mF | Genus |
α | { 2n+1, 4n+2 }2 | 1, 2, 2n+1 | 4n+2,2n+1 | n |
α' | { 4n+2, 2n+1 }2 | 2, 1, 2n+1 | 2n+1,4n+2 |
α'° | { 2, 2n+1 }4n+2 | 2, 2n+1, 2n+1 | 2n+1,1 | 0 |
α'°' | { 2n+1, 2 }4n+2 | 2n+1, 2, 2n+1 | 1,2n+1 |
α°' | { 4n+2, 2 }2n+1 | 2n+1, 1, 2n+1 | 1,4n+2 | 1 |
α° | { 2, 4n+2 }2n+1 | 1, 2n+1, 2n+1 | 4n+2,1 |
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α'° is the 2n+1-hosohedron.
α'°' is the di-2n+1-gon.
α°' is the hemi-di-4n+2-gon.
α° is the hemi-4n+2-hosohedron.
γ° is the 2n+1-hosohedron.
γ°' is the di-2n+1-gon.
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Β | n > 0, no. of edges is even |
name | Schläfli formula | Vertices, Faces, Edges | mV,mF | Genus |
β | { 4n, 4n }2 | 1, 1, 2n | 4n,4n | n |
β° | { 2, 4n }4n | 1, 2n, 2n | 4n,1 | 1 |
β°' | { 4n, 2 }4n | 2n, 1, 2n | n |
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Γ | n ≥ 0, no. of edges is even |
name | Schläfli formula | Vertices, Faces, Edges | mV,mF | Genus |
γ | { 2n+2, 2n+2 }2 | 2, 2, 2n+2 | 2n+2,2n+2 | n |
γ° | { 2, 2n+2 }2n+2 | 2, 2n+2, 2n+2 | 2n+2,1 | 0 |
γ°' | { 2n+2, 2 }2n+2 | 2n+2, 2, 2n+2 | 1,2n+2 |
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Δ | n = ±1 modulo 6, no. of edges is odd |
name | Schläfli formula | Vertices, Faces, Edges | mV,mF | Genus |
δ | { 6, 3n }2n | 2, n, 3n | 3n,3 | n |
δ' | { 3n, 6 }2n | n, 2, 3n | 3,3n |
δ'° | { 2n, 6 }3n | n, 3, 3n | 3,n | 2n-1 |
δ'°' | { 6, 2n }3n | 3, n, 3n | n,3 |
δ°' | { 3n, 2n }6 | 3, 2, 3n | n,3n | (n-1)*3/2 |
δ° | { 2n, 3n }6 | 2, 3, 3n | 3n,n |
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Ε | n = ±2 modulo 6, no. of edges is even |
name | Schläfli formula | Vertices, Faces, Edges | mV,mF | Genus |
ε | { 6, 3n }n | 2, n, 3n | 3n,3 | n |
ε' | { 3n, 6 }n | n, 2, 3n | 3,3n |
ε'° | { n, 6 }3n | n, 6, 3n | 3,n/2 | n-2 |
ε'°' | { 6, n }3n | 6, n, 3n | n/2,3 |
ε°' | { 3n, n }6 | 6, 2, 3n | n/2,3n | (n-2)*3/2 |
ε° | { n, 3n }6 | 2, 6, 3n | 3n,n/2 |
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Ζ | n even, no. of edges modulo 8 is 4 |
name | Schläfli formula | Vertices, Faces, Edges | mV,mF | Genus |
ζ | { 4, 2n+2 }4n+4 | 4, 2n+2, 4n+4 | n+1,2 | n |
ζ' | { 2n+2, 4 }4n+4 | 2n+2, 4, 4n+4 | 2,n+1 |
ζ'° | { 4n+4, 4 }2n+2 | 2n+2, 2, 4n+4 | 2,4n+4 | n+1 |
ζ'°' | { 4, 4n+4 }2n+2 | 2, 2n+2, 4n+4 | 4n+4,2 |
ζ°' | { 2n+2, 4n+4 }4 | 2, 4, 4n+4 | 4n+4,n+1 | 2n |
ζ° | { 4n+4, 2n+2 }4 | 4, 2, 4n+4 | n+1,4n+4 |
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Η | n even and positive, no. of edges modulo 8 is 0 |
name | Schläfli formula | Vertices, Faces, Edges | mV, mF | Genus |
η | { 4, 4n }4n | 2, 2n, 4n | 4n, 2 | n |
η' | { 4n, 4 }4n | 2n, 4, 4n | 2,4n |
η° | { 4n, 4n }4 | 2, 2, 4n | 4n,4n | 2n-1 |
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Θ | n even, no. of edges modulo 8 is 0 |
name | Schläfli formula | Vertices, Faces, Edges | mV, mF | Genus |
θ | { 4, 2n }2n | 4, 2n, 4n | n, 2 | n-1 |
θ' | { 2n, 4 }2n | 2n, 4, 4n | 2, n |
θ° | { 2n, 2n }4 | 4, 4, 4n | n, n | 2n-3 |
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Ι | n > 0, no. of edges modulo 16 is 0 |
name | Schläfli formula | Vertices, Faces, Edges | mV, mF | Genus |
ι | { 4, 8n }4 | 4, 8n, 16n | 4n, 1 | 4n-1 |
ι' | { 8n, 4 }4 | 8n, 4, 16n | 1, 4n |
ι° | { 4, 4 }8n | 4, 4, 16n | 4n, 4n | 8n-3 |
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For λ2, mV=mF=2
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Κ | n odd, no. of edges modulo 4 is 2 |
name | Schläfli formula | Vertices, Faces, Edges | mV,mF | Genus |
κ |
{ 4, 2n }4 |
2n, n2, 2n2 |
2,1 |
n2-2n+2 |
κ' |
{ 2n, 4 }4 |
n2, 2n,2n2 |
1,2 |
κ'° |
{ 4, 4 }2n {n,0) |
n2, n2, 2n2 |
1,1 |
1 |
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For κ2, mF=4.
For κ'2, mV=4.
For κ'°2, mV=mF=4.
For μ2, mF=4.
For μ'2, mV=4.
For μ'°2, mV=mF=4.
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Λ | n>0, n even, no. of edges modulo 8 is 0 |
name | Schläfli formula | Vertices, Faces, Edges | mV,mF | Genus |
λ |
{ 4, 2n }4 |
2n, n2, 2n2 |
2,1 |
n2/2-n+1 |
λ' |
{ 2n, 4 }4 |
n2, 2n,2n2 |
1,2 |
λ'° |
{ 4, 4 }2n (n,0) |
n2, n2, 2n2 |
1,1 |
1 |
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Μ | n>0, n even, no. of edges modulo 16 is 0 |
name | Schläfli formula | Vertices, Faces, Edges | mV,mF | Genus |
μ |
{ 4, 2n }4 |
4n, 2n2, 4n2 |
1,1 |
(n-1)2 |
μ' |
{ 2n, 4 }4 |
2n2, 4n, 4n2 |
1,1 |
μ'° |
{ 4, 4 }2n (n,n) |
2n2, 2n2, 4n2 |
1,1 |
1 |
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Ν | n > 0, no. of edges modulo 6 is 0 |
name | Schläfli formula | Vertices, Faces, Edges | mV, mF | Genus |
ν |
{ 4, 3n }3n |
4, 3n, 6n |
n,2 |
3n-2 |
ν' |
{ 3n, 4 }3n |
3n, 4, 6n |
2,n |
ν° |
{ 3n, 3n }4 |
4, 4, 6n |
n, n |
3n-3 |
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