Polytope of Type {6,10}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {6,10}*1500b
if this polytope has a name.
Group : SmallGroup(1500,125)
Rank : 3
Schlafli Type : {6,10}
Number of vertices, edges, etc : 75, 375, 125
Order of s₀s₁s₂ : 15
Order of s₀s₁s₂s₁ : 10
Special Properties :
   Compact Hyperbolic Quotient
   Locally Spherical
   Non-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 : {6,10}*300
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

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

Permutation Representation (Magma) :

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

References : None.
to this polytope