Polytope of Type {15,30} with group SmallGroup(1200,983)

Overview

Group: SmallGroup(1200,983)
Rank: 3
Schläfli Type: {15,30}
Vertices, edges, …: 20, 300, 40
Order of s₀s₁s₂: 20
Order of s₀s₁s₂s₁: 30
Also known as: if this polytope has a name.

Special Properties

Compact Hyperbolic Quotient
Locally Spherical
Orientable

Quotients maximal quotients in bold

5-fold

{15,6}*240

12-fold

{5,10}*100

25-fold

{3,6}*48

50-fold

{3,3}*24

60-fold

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

Permutation Representation (Magma)

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

References