Polytope of Type {12,12} with group SmallGroup(1920,240806)

Overview

Group: SmallGroup(1920,240806)
Rank: 3
Schläfli Type: {12,12}
Vertices, edges, …: 80, 480, 80
Order of s₀s₁s₂: 12
Order of s₀s₁s₂s₁: 20
Also known as: if this polytope has a name.

Special Properties

Compact Hyperbolic Quotient
Locally Spherical
Orientable
Self-Petrie

Quotients maximal quotients in bold

2-fold

4-fold

8-fold

16-fold

{6,6}*120

120-fold

{4,2}*16

240-fold

{2,2}*8

Covers minimal covers in bold

None in this atlas.

Irregular Quotients of which this is a minimal cover

Click an entry to reveal its facets and vertex figures.

P/N, where N=<s1*s0*s1*s2*s1*s0*(s1*s2)^3> of order 5

16 facets

16 of {12}*24

16 vertex figures

16 of {12}*24

Representations

Permutation Representation (GAP)

s0 := (  3,  4)(  7, 48)(  8, 47)(  9, 10)( 13, 14)( 15, 16)( 17, 51)( 18, 52)( 19, 33)( 20, 34)( 21, 22)( 23, 49)( 24, 50)( 25, 46)( 26, 45)( 31, 37)( 32, 38)( 35, 44)( 36, 43)( 39, 41)( 40, 42)( 55, 56)( 57, 58)( 59, 99)( 60,100)( 63, 64)( 69,104)( 70,103)( 71, 86)( 72, 85)( 75,102)( 76,101)( 77, 97)( 78, 98)( 79, 80)( 81, 82)( 83, 90)( 84, 89)( 87, 95)( 88, 96)( 91, 94)( 92, 93);;
s1 := (  1, 55)(  2, 56)(  3, 53)(  4, 54)(  5, 69)(  6, 70)(  7, 64)(  8, 63)(  9, 84)( 10, 83)( 11, 59)( 12, 60)( 13,101)( 14,102)( 15, 97)( 16, 98)( 17, 58)( 18, 57)( 19, 73)( 20, 74)( 21, 72)( 22, 71)( 23, 89)( 24, 90)( 25, 86)( 26, 85)( 27, 92)( 28, 91)( 29, 88)( 30, 87)( 31, 61)( 32, 62)( 33, 77)( 34, 78)( 35, 81)( 36, 82)( 37, 76)( 38, 75)( 39, 79)( 40, 80)( 41, 99)( 42,100)( 43,103)( 44,104)( 45, 68)( 46, 67)( 47, 94)( 48, 93)( 49, 66)( 50, 65)( 51, 96)( 52, 95);;
s2 := (  1, 53)(  2, 54)(  3, 55)(  4, 56)(  5, 65)(  6, 66)(  7,100)(  8, 99)(  9, 79)( 10, 80)( 11, 68)( 12, 67)( 13, 58)( 14, 57)( 15, 63)( 16, 64)( 17,103)( 18,104)( 19, 86)( 20, 85)( 21, 81)( 22, 82)( 23, 77)( 24, 78)( 25, 76)( 26, 75)( 27, 62)( 28, 61)( 29, 74)( 30, 73)( 31, 90)( 32, 89)( 33, 71)( 34, 72)( 35, 92)( 36, 91)( 37, 83)( 38, 84)( 39, 87)( 40, 88)( 41, 95)( 42, 96)( 43, 94)( 44, 93)( 45,102)( 46,101)( 47, 59)( 48, 60)( 49, 97)( 50, 98)( 51, 70)( 52, 69);;
poly := Group([s0,s1,s2]);;

Finitely Presented Group Representation (GAP)

F := FreeGroup("s0","s1","s2");;
s0 := F.1;;  s1 := F.2;;  s2 := F.3;;  
rels := [ s0*s0, s1*s1, s2*s2, s0*s2*s0*s2, s0*s1*s2*s1*s2*s1*s0*s1*s0*s2*s1*s2*s1*s2*s1*s0*s2*s1, 
s0*s1*s0*s1*s2*s0*s1*s0*s1*s2*s1*s0*s1*s0*s1*s2*s1*s0*s1*s2*s0*s1 ];;
poly := F / rels;;

Permutation Representation (Magma)

s0 := Sym(104)!(  3,  4)(  7, 48)(  8, 47)(  9, 10)( 13, 14)( 15, 16)( 17, 51)( 18, 52)( 19, 33)( 20, 34)( 21, 22)( 23, 49)( 24, 50)( 25, 46)( 26, 45)( 31, 37)( 32, 38)( 35, 44)( 36, 43)( 39, 41)( 40, 42)( 55, 56)( 57, 58)( 59, 99)( 60,100)( 63, 64)( 69,104)( 70,103)( 71, 86)( 72, 85)( 75,102)( 76,101)( 77, 97)( 78, 98)( 79, 80)( 81, 82)( 83, 90)( 84, 89)( 87, 95)( 88, 96)( 91, 94)( 92, 93);
s1 := Sym(104)!(  1, 55)(  2, 56)(  3, 53)(  4, 54)(  5, 69)(  6, 70)(  7, 64)(  8, 63)(  9, 84)( 10, 83)( 11, 59)( 12, 60)( 13,101)( 14,102)( 15, 97)( 16, 98)( 17, 58)( 18, 57)( 19, 73)( 20, 74)( 21, 72)( 22, 71)( 23, 89)( 24, 90)( 25, 86)( 26, 85)( 27, 92)( 28, 91)( 29, 88)( 30, 87)( 31, 61)( 32, 62)( 33, 77)( 34, 78)( 35, 81)( 36, 82)( 37, 76)( 38, 75)( 39, 79)( 40, 80)( 41, 99)( 42,100)( 43,103)( 44,104)( 45, 68)( 46, 67)( 47, 94)( 48, 93)( 49, 66)( 50, 65)( 51, 96)( 52, 95);
s2 := Sym(104)!(  1, 53)(  2, 54)(  3, 55)(  4, 56)(  5, 65)(  6, 66)(  7,100)(  8, 99)(  9, 79)( 10, 80)( 11, 68)( 12, 67)( 13, 58)( 14, 57)( 15, 63)( 16, 64)( 17,103)( 18,104)( 19, 86)( 20, 85)( 21, 81)( 22, 82)( 23, 77)( 24, 78)( 25, 76)( 26, 75)( 27, 62)( 28, 61)( 29, 74)( 30, 73)( 31, 90)( 32, 89)( 33, 71)( 34, 72)( 35, 92)( 36, 91)( 37, 83)( 38, 84)( 39, 87)( 40, 88)( 41, 95)( 42, 96)( 43, 94)( 44, 93)( 45,102)( 46,101)( 47, 59)( 48, 60)( 49, 97)( 50, 98)( 51, 70)( 52, 69);
poly := sub<Sym(104)|s0,s1,s2>;

Finitely Presented Group Representation (Magma)

poly<s0,s1,s2> := Group< s0,s1,s2 | s0*s0, s1*s1, s2*s2, 
s0*s2*s0*s2, s0*s1*s2*s1*s2*s1*s0*s1*s0*s2*s1*s2*s1*s2*s1*s0*s2*s1, 
s0*s1*s0*s1*s2*s0*s1*s0*s1*s2*s1*s0*s1*s0*s1*s2*s1*s0*s1*s2*s0*s1 >;

References

None.

to this polytope.