Polytope of Type {15,10} with group SmallGroup(1500,37)

Overview

Group: SmallGroup(1500,37)
Rank: 3
Schläfli Type: {15,10}
Vertices, edges, …: 75, 375, 50
Order of s₀s₁s₂: 6
Order of s₀s₁s₂s₁: 10
Also known as: if this polytope has a name.

Special Properties

Compact Hyperbolic Quotient
Locally Spherical
Orientable

Quotients maximal quotients in bold

5-fold

{3,10}*300

125-fold

{3,2}*12

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

10 facets

10 of {15}*30

15 vertex figures

15 of {10}*20

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

References

None.

to this polytope.