Polytope of Type {10,15}

Play with this polytope as a twisty puzzle

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {10,15}*1500g
if this polytope has a name.
Group : SmallGroup(1500,126)
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
   25-fold quotients : {2,15}*60
   75-fold quotients : {2,5}*20
   125-fold quotients : {2,3}*12
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> of order 5.
      35 facets:
         25 of {2}*4
         10 of {10}*20
      10 vertex figures:
         10 of {15}*30
   P/N, where N=<s0*s1*s0*s1*s0*s2*s1*s0*s1*s2> of order 5.
      15 facets:
         15 of {10}*20
      10 vertex figures:
         10 of {15}*30
   P/N, where N=<s0*s1*s0*s1*s0*s2*s1*s0*s2*s1*s2*s1> of order 5.
      15 facets:
         15 of {10}*20
      10 vertex figures:
         10 of {15}*30
   P/N, where N=<s0*s1*s0*s1*s0*s1*s0*s1*s0*s2*s1*s0*s2*s1*s2*s1> of order 5.
      15 facets:
         15 of {10}*20
      10 vertex figures:
         10 of {15}*30

Permutation Representation (GAP) : 
s0 := (  2,  5)(  3,  4)(  6, 21)(  7, 25)(  8, 24)(  9, 23)( 10, 22)( 11, 16)( 12, 20)( 13, 19)( 14, 18)( 15, 17)( 27, 30)( 28, 29)( 31, 46)( 32, 50)( 33, 49)( 34, 48)( 35, 47)( 36, 41)( 37, 45)( 38, 44)( 39, 43)( 40, 42)( 52, 55)( 53, 54)( 56, 71)( 57, 75)( 58, 74)( 59, 73)( 60, 72)( 61, 66)( 62, 70)( 63, 69)( 64, 68)( 65, 67)( 77, 80)( 78, 79)( 81, 96)( 82,100)( 83, 99)( 84, 98)( 85, 97)( 86, 91)( 87, 95)( 88, 94)( 89, 93)( 90, 92)(102,105)(103,104)(106,121)(107,125)(108,124)(109,123)(110,122)(111,116)(112,120)(113,119)(114,118)(115,117);;
s1 := (  1,  2)(  3,  5)(  6,  8)(  9, 10)( 11, 14)( 12, 13)( 16, 20)( 17, 19)( 22, 25)( 23, 24)( 26,102)( 27,101)( 28,105)( 29,104)( 30,103)( 31,108)( 32,107)( 33,106)( 34,110)( 35,109)( 36,114)( 37,113)( 38,112)( 39,111)( 40,115)( 41,120)( 42,119)( 43,118)( 44,117)( 45,116)( 46,121)( 47,125)( 48,124)( 49,123)( 50,122)( 51, 77)( 52, 76)( 53, 80)( 54, 79)( 55, 78)( 56, 83)( 57, 82)( 58, 81)( 59, 85)( 60, 84)( 61, 89)( 62, 88)( 63, 87)( 64, 86)( 65, 90)( 66, 95)( 67, 94)( 68, 93)( 69, 92)( 70, 91)( 71, 96)( 72,100)( 73, 99)( 74, 98)( 75, 97);;
s2 := (  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);;
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*s1*s0*s1*s2*s1*s0*s1*s0*s1*s2*s1*s0*s1*s0*s2*s1*s0, 
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 ];;
poly := F / rels;;
Permutation Representation (Magma) : 
s0 := Sym(125)!(  2,  5)(  3,  4)(  6, 21)(  7, 25)(  8, 24)(  9, 23)( 10, 22)( 11, 16)( 12, 20)( 13, 19)( 14, 18)( 15, 17)( 27, 30)( 28, 29)( 31, 46)( 32, 50)( 33, 49)( 34, 48)( 35, 47)( 36, 41)( 37, 45)( 38, 44)( 39, 43)( 40, 42)( 52, 55)( 53, 54)( 56, 71)( 57, 75)( 58, 74)( 59, 73)( 60, 72)( 61, 66)( 62, 70)( 63, 69)( 64, 68)( 65, 67)( 77, 80)( 78, 79)( 81, 96)( 82,100)( 83, 99)( 84, 98)( 85, 97)( 86, 91)( 87, 95)( 88, 94)( 89, 93)( 90, 92)(102,105)(103,104)(106,121)(107,125)(108,124)(109,123)(110,122)(111,116)(112,120)(113,119)(114,118)(115,117);
s1 := Sym(125)!(  1,  2)(  3,  5)(  6,  8)(  9, 10)( 11, 14)( 12, 13)( 16, 20)( 17, 19)( 22, 25)( 23, 24)( 26,102)( 27,101)( 28,105)( 29,104)( 30,103)( 31,108)( 32,107)( 33,106)( 34,110)( 35,109)( 36,114)( 37,113)( 38,112)( 39,111)( 40,115)( 41,120)( 42,119)( 43,118)( 44,117)( 45,116)( 46,121)( 47,125)( 48,124)( 49,123)( 50,122)( 51, 77)( 52, 76)( 53, 80)( 54, 79)( 55, 78)( 56, 83)( 57, 82)( 58, 81)( 59, 85)( 60, 84)( 61, 89)( 62, 88)( 63, 87)( 64, 86)( 65, 90)( 66, 95)( 67, 94)( 68, 93)( 69, 92)( 70, 91)( 71, 96)( 72,100)( 73, 99)( 74, 98)( 75, 97);
s2 := 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);
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*s1*s0*s1*s2*s1*s0*s1*s0*s1*s2*s1*s0*s1*s0*s2*s1*s0, 
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 >;
References : None.
to this polytope

Twisty Puzzle