Polytope of Type {10,3} with group SmallGroup(1500,37)

Overview

Group: SmallGroup(1500,37)
Rank: 3
Schläfli Type: {10,3}
Vertices, edges, …: 250, 375, 75
Order of s₀s₁s₂: 30
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

{10,3}*300

125-fold

{2,3}*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)^4*s2*(s1*s0)^2*s2> of order 5

15 facets

15 of {10}*20

50 vertex figures

50 of {3}*6

P/N, where N=<(s0*s1)^2> of order 5

19 facets

5 of {2}*4
14 of {10}*20

50 vertex figures

50 of {3}*6

Representations

Permutation Representation (GAP)

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

Permutation Representation (Magma)

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

References

None.

to this polytope.