Polytope of Type {10,15}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {10,15}*1500c
if this polytope has a name.
Group : SmallGroup(1500,37)
Rank : 3
Schlafli Type : {10,15}
Number of vertices, edges, etc : 50, 375, 75
Order of s₀s₁s₂ : 30
Order of s₀s₁s₂s₁ : 10
Special Properties :
   Compact Hyperbolic Quotient
   Locally Spherical
   Orientable
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   None in this Atlas
Vertex Figure Of :
   None in this Atlas
Quotients (Maximal Quotients in Boldface) :
   5-fold quotients : {10,3}*300
   125-fold quotients : {2,3}*12
Covers (Minimal Covers in Boldface) :
   None in this atlas.
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,  3)(  4,  5)(  7, 10)(  8,  9)( 11, 14)( 12, 13)( 16, 17)( 18, 20)
( 21, 25)( 22, 24)( 26,114)( 27,113)( 28,112)( 29,111)( 30,115)( 31,117)
( 32,116)( 33,120)( 34,119)( 35,118)( 36,125)( 37,124)( 38,123)( 39,122)
( 40,121)( 41,103)( 42,102)( 43,101)( 44,105)( 45,104)( 46,106)( 47,110)
( 48,109)( 49,108)( 50,107)( 51, 96)( 52,100)( 53, 99)( 54, 98)( 55, 97)
( 56, 79)( 57, 78)( 58, 77)( 59, 76)( 60, 80)( 61, 82)( 62, 81)( 63, 85)
( 64, 84)( 65, 83)( 66, 90)( 67, 89)( 68, 88)( 69, 87)( 70, 86)( 71, 93)
( 72, 92)( 73, 91)( 74, 95)( 75, 94);;
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*s2*s1*s0*s1*s2*s1*s2*s1, 
s2*s0*s1*s0*s1*s2*s1*s0*s1*s2*s0*s1*s2*s0*s1*s2*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(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,  3)(  4,  5)(  7, 10)(  8,  9)( 11, 14)( 12, 13)( 16, 17)
( 18, 20)( 21, 25)( 22, 24)( 26,114)( 27,113)( 28,112)( 29,111)( 30,115)
( 31,117)( 32,116)( 33,120)( 34,119)( 35,118)( 36,125)( 37,124)( 38,123)
( 39,122)( 40,121)( 41,103)( 42,102)( 43,101)( 44,105)( 45,104)( 46,106)
( 47,110)( 48,109)( 49,108)( 50,107)( 51, 96)( 52,100)( 53, 99)( 54, 98)
( 55, 97)( 56, 79)( 57, 78)( 58, 77)( 59, 76)( 60, 80)( 61, 82)( 62, 81)
( 63, 85)( 64, 84)( 65, 83)( 66, 90)( 67, 89)( 68, 88)( 69, 87)( 70, 86)
( 71, 93)( 72, 92)( 73, 91)( 74, 95)( 75, 94);
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*s2*s1*s2*s1*s0*s1*s2*s1*s2*s1, 
s2*s0*s1*s0*s1*s2*s1*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1, 
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 >;

References : None.
to this polytope