Polytope of Type {6,15}

Play with this polytope as a twisty puzzle

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {6,15}*1500b
if this polytope has a name.
Group : SmallGroup(1500,125)
Rank : 3
Schlafli Type : {6,15}
Number of vertices, edges, etc : 50, 375, 125
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 : {6,3}*300
   75-fold quotients : {2,5}*20
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Irregular Quotients (of which this is a minimal cover):
   P/N, where N=<s0*s1*s0*s1*s0*s2*s1*s0*s1*s2> of order 5.
      25 facets:
         25 of {6}*12
      10 vertex figures:
         10 of {15}*30
   P/N, where N=<s0*s1*s0*s1*s2*s1*s0*s2*s1*s0*s2*s1> of order 5.
      25 facets:
         25 of {6}*12
      10 vertex figures:
         10 of {15}*30
   P/N, where N=<s0*s1*s0*s2*s1*s0*s1*s0*s2*s1*s0*s2*s1*s0*s2*s1> of order 5.
      25 facets:
         25 of {6}*12
      10 vertex figures:
         10 of {15}*30

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, 33)(  7, 32)(  8, 31)(  9, 35)( 10, 34)( 11, 39)( 12, 38)( 13, 37)( 14, 36)( 15, 40)( 16, 45)( 17, 44)( 18, 43)( 19, 42)( 20, 41)( 21, 46)( 22, 50)( 23, 49)( 24, 48)( 25, 47)( 51,102)( 52,101)( 53,105)( 54,104)( 55,103)( 56,108)( 57,107)( 58,106)( 59,110)( 60,109)( 61,114)( 62,113)( 63,112)( 64,111)( 65,115)( 66,120)( 67,119)( 68,118)( 69,117)( 70,116)( 71,121)( 72,125)( 73,124)( 74,123)( 75,122)( 76, 77)( 78, 80)( 81, 83)( 84, 85)( 86, 89)( 87, 88)( 91, 95)( 92, 94)( 97,100)( 98, 99);;
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, 
s0*s1*s2*s1*s2*s1*s0*s1*s2*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*s2*s1*s0*s1*s0*s1*s2*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, 33)(  7, 32)(  8, 31)(  9, 35)( 10, 34)( 11, 39)( 12, 38)( 13, 37)( 14, 36)( 15, 40)( 16, 45)( 17, 44)( 18, 43)( 19, 42)( 20, 41)( 21, 46)( 22, 50)( 23, 49)( 24, 48)( 25, 47)( 51,102)( 52,101)( 53,105)( 54,104)( 55,103)( 56,108)( 57,107)( 58,106)( 59,110)( 60,109)( 61,114)( 62,113)( 63,112)( 64,111)( 65,115)( 66,120)( 67,119)( 68,118)( 69,117)( 70,116)( 71,121)( 72,125)( 73,124)( 74,123)( 75,122)( 76, 77)( 78, 80)( 81, 83)( 84, 85)( 86, 89)( 87, 88)( 91, 95)( 92, 94)( 97,100)( 98, 99);
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, 
s0*s1*s2*s1*s2*s1*s0*s1*s2*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*s2*s1*s0*s1*s0*s1*s2*s1 >;
References : None.
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