Polytope of Type {15,6} with group SmallGroup(1500,37)

Overview

Group: SmallGroup(1500,37)
Rank: 3
Schläfli Type: {15,6}
Vertices, edges, …: 125, 375, 50
Order of s₀s₁s₂: 10
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

{3,6}*300

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=<s0*s1*s2*s1*s0*(s2*s1)^2*s2> of order 5

10 facets

10 of {15}*30

25 vertex figures

25 of {6}*12

Representations

Permutation Representation (GAP)

s0 := (  2,  5)(  3,  4)(  6, 35)(  7, 34)(  8, 33)(  9, 32)( 10, 31)( 11, 61)( 12, 65)( 13, 64)( 14, 63)( 15, 62)( 16, 94)( 17, 93)( 18, 92)( 19, 91)( 20, 95)( 21,124)( 22,123)( 23,122)( 24,121)( 25,125)( 26,101)( 27,105)( 28,104)( 29,103)( 30,102)( 37, 40)( 38, 39)( 41, 69)( 42, 68)( 43, 67)( 44, 66)( 45, 70)( 46, 99)( 47, 98)( 48, 97)( 49, 96)( 50,100)( 51, 76)( 52, 80)( 53, 79)( 54, 78)( 55, 77)( 56,110)( 57,109)( 58,108)( 59,107)( 60,106)( 71, 74)( 72, 73)( 81, 85)( 82, 84)( 86,111)( 87,115)( 88,114)( 89,113)( 90,112)(116,119)(117,118);;
s1 := (  1,  2)(  3,  5)(  6, 10)(  7,  9)( 11, 13)( 14, 15)( 17, 20)( 18, 19)( 21, 24)( 22, 23)( 26,113)( 27,112)( 28,111)( 29,115)( 30,114)( 31,116)( 32,120)( 33,119)( 34,118)( 35,117)( 36,124)( 37,123)( 38,122)( 39,121)( 40,125)( 41,102)( 42,101)( 43,105)( 44,104)( 45,103)( 46,110)( 47,109)( 48,108)( 49,107)( 50,106)( 51,100)( 52, 99)( 53, 98)( 54, 97)( 55, 96)( 56, 78)( 57, 77)( 58, 76)( 59, 80)( 60, 79)( 61, 81)( 62, 85)( 63, 84)( 64, 83)( 65, 82)( 66, 89)( 67, 88)( 68, 87)( 69, 86)( 70, 90)( 71, 92)( 72, 91)( 73, 95)( 74, 94)( 75, 93);;
s2 := (  1, 36)(  2, 40)(  3, 39)(  4, 38)(  5, 37)(  6, 10)(  7,  9)( 11,101)( 12,105)( 13,104)( 14,103)( 15,102)( 16, 99)( 17, 98)( 18, 97)( 19, 96)( 20,100)( 21, 69)( 22, 68)( 23, 67)( 24, 66)( 25, 70)( 26, 61)( 27, 65)( 28, 64)( 29, 63)( 30, 62)( 31, 35)( 32, 34)( 41,124)( 42,123)( 43,122)( 44,121)( 45,125)( 46, 94)( 47, 93)( 48, 92)( 49, 91)( 50, 95)( 51, 86)( 52, 90)( 53, 89)( 54, 88)( 55, 87)( 56, 60)( 57, 59)( 71,119)( 72,118)( 73,117)( 74,116)( 75,120)( 76,111)( 77,115)( 78,114)( 79,113)( 80,112)( 81, 85)( 82, 84)(106,110)(107,109);;
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, 
s0*s1*s0*s1*s2*s0*s1*s0*s1*s0*s1*s2*s0*s1, 
s1*s2*s0*s1*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s0, 
s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1 ];;
poly := F / rels;;

Permutation Representation (Magma)

s0 := Sym(125)!(  2,  5)(  3,  4)(  6, 35)(  7, 34)(  8, 33)(  9, 32)( 10, 31)( 11, 61)( 12, 65)( 13, 64)( 14, 63)( 15, 62)( 16, 94)( 17, 93)( 18, 92)( 19, 91)( 20, 95)( 21,124)( 22,123)( 23,122)( 24,121)( 25,125)( 26,101)( 27,105)( 28,104)( 29,103)( 30,102)( 37, 40)( 38, 39)( 41, 69)( 42, 68)( 43, 67)( 44, 66)( 45, 70)( 46, 99)( 47, 98)( 48, 97)( 49, 96)( 50,100)( 51, 76)( 52, 80)( 53, 79)( 54, 78)( 55, 77)( 56,110)( 57,109)( 58,108)( 59,107)( 60,106)( 71, 74)( 72, 73)( 81, 85)( 82, 84)( 86,111)( 87,115)( 88,114)( 89,113)( 90,112)(116,119)(117,118);
s1 := Sym(125)!(  1,  2)(  3,  5)(  6, 10)(  7,  9)( 11, 13)( 14, 15)( 17, 20)( 18, 19)( 21, 24)( 22, 23)( 26,113)( 27,112)( 28,111)( 29,115)( 30,114)( 31,116)( 32,120)( 33,119)( 34,118)( 35,117)( 36,124)( 37,123)( 38,122)( 39,121)( 40,125)( 41,102)( 42,101)( 43,105)( 44,104)( 45,103)( 46,110)( 47,109)( 48,108)( 49,107)( 50,106)( 51,100)( 52, 99)( 53, 98)( 54, 97)( 55, 96)( 56, 78)( 57, 77)( 58, 76)( 59, 80)( 60, 79)( 61, 81)( 62, 85)( 63, 84)( 64, 83)( 65, 82)( 66, 89)( 67, 88)( 68, 87)( 69, 86)( 70, 90)( 71, 92)( 72, 91)( 73, 95)( 74, 94)( 75, 93);
s2 := Sym(125)!(  1, 36)(  2, 40)(  3, 39)(  4, 38)(  5, 37)(  6, 10)(  7,  9)( 11,101)( 12,105)( 13,104)( 14,103)( 15,102)( 16, 99)( 17, 98)( 18, 97)( 19, 96)( 20,100)( 21, 69)( 22, 68)( 23, 67)( 24, 66)( 25, 70)( 26, 61)( 27, 65)( 28, 64)( 29, 63)( 30, 62)( 31, 35)( 32, 34)( 41,124)( 42,123)( 43,122)( 44,121)( 45,125)( 46, 94)( 47, 93)( 48, 92)( 49, 91)( 50, 95)( 51, 86)( 52, 90)( 53, 89)( 54, 88)( 55, 87)( 56, 60)( 57, 59)( 71,119)( 72,118)( 73,117)( 74,116)( 75,120)( 76,111)( 77,115)( 78,114)( 79,113)( 80,112)( 81, 85)( 82, 84)(106,110)(107,109);
poly := sub<Sym(125)|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, 
s0*s1*s0*s1*s2*s0*s1*s0*s1*s0*s1*s2*s0*s1, 
s1*s2*s0*s1*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s0, 
s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1 >;

References

None.

to this polytope.