Polytope of Type {15,6}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {15,6}*1500b
if this polytope has a name.
Group : SmallGroup(1500,125)
Rank : 3
Schlafli Type : {15,6}
Number of vertices, edges, etc : 125, 375, 50
Order of s₀s₁s₂ : 10
Order of s₀s₁s₂s₁ : 6
Special Properties :
   Compact Hyperbolic Quotient
   Locally Spherical
   Orientable
Related Polytopes :
   Facet
   Vertex Figure
   Dual
   Petrial
Facet Of :
   None in this Atlas
Vertex Figure Of :
   None in this Atlas
Quotients (Maximal Quotients in Boldface) :
   5-fold quotients : {3,6}*300
   75-fold quotients : {5,2}*20
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

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

Permutation Representation (Magma) :

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

References : None.
to this polytope