Polytope of Type {10,30}

Play with this polytope as a twisty puzzle

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {10,30}*1500c
if this polytope has a name.
Group : SmallGroup(1500,37)
Rank : 3
Schlafli Type : {10,30}
Number of vertices, edges, etc : 25, 375, 75
Order of s0s1s2 : 3
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 : {10,6}*300
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Irregular Quotients (of which this is a minimal cover):
   None.

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

Twisty Puzzle