Polytope of Type {30,20} with group SmallGroup(1200,983)

Overview

Group: SmallGroup(1200,983)
Rank: 3
Schläfli Type: {30,20}
Vertices, edges, …: 30, 300, 20
Order of s₀s₁s₂: 15
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

10-fold

{15,4}*120

25-fold

{6,4}*48b

50-fold

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

Permutation Representation (Magma)

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

References