Polytope of Type {6,75} with group SmallGroup(1200,195)

Overview

Group: SmallGroup(1200,195)
Rank: 3
Schläfli Type: {6,75}
Vertices, edges, …: 8, 300, 100
Order of s₀s₁s₂: 100
Order of s₀s₁s₂s₁: 6
Also known as: if this polytope has a name.

Special Properties

Compact Hyperbolic Quotient
Locally Spherical
Orientable

Quotients maximal quotients in bold

5-fold

{6,15}*240

12-fold

{2,25}*100

25-fold

{6,3}*48

50-fold

{3,3}*24

60-fold

{2,5}*20

Covers minimal covers in bold

None in this atlas.

Irregular Quotients of which this is a minimal cover

None.

Representations

Permutation Representation (GAP)

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

Permutation Representation (Magma)

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

References