Polytope of Type {100,6} with group SmallGroup(1200,195)

Overview

Group: SmallGroup(1200,195)
Rank: 3
Schläfli Type: {100,6}
Vertices, edges, …: 100, 300, 6
Order of s₀s₁s₂: 75
Order of s₀s₁s₂s₁: 4
Also known as: if this polytope has a name.

Special Properties

Compact Hyperbolic Quotient
Locally Spherical
Non-Orientable
Flat

Quotients maximal quotients in bold

5-fold

{20,6}*240b

25-fold

{4,6}*48b

50-fold

{4,3}*24

Covers minimal covers in bold

None in this atlas.

Irregular Quotients of which this is a minimal cover

None.

Representations

Permutation Representation (GAP)

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

Permutation Representation (Magma)

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

References