Polytope of Type {10,20}

Play with this polytope as a twisty puzzle

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {10,20}*1000b
if this polytope has a name.
Group : SmallGroup(1000,92)
Rank : 3
Schlafli Type : {10,20}
Number of vertices, edges, etc : 25, 250, 50
Order of s₀s₁s₂ : 4
Order of s₀s₁s₂s₁ : 10
Special Properties :
   Compact Hyperbolic Quotient
   Locally Spherical
   Non-Orientable
Related Polytopes :
   Facet
   Vertex Figure
   Dual
   Petrial
Facet Of :
   {10,20,2} of size 2000
Vertex Figure Of :
   {2,10,20} of size 2000
Quotients (Maximal Quotients in Boldface) :
   5-fold quotients : {10,4}*200
Covers (Minimal Covers in Boldface) :
   2-fold covers : {10,20}*2000f
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, 58)(  7, 57)(  8, 56)(  9, 60)( 10, 59)( 11, 86)( 12, 90)( 13, 89)( 14, 88)( 15, 87)( 16,120)( 17,119)( 18,118)( 19,117)( 20,116)( 21, 25)( 22, 24)( 31, 33)( 34, 35)( 36, 61)( 37, 65)( 38, 64)( 39, 63)( 40, 62)( 41, 95)( 42, 94)( 43, 93)( 44, 92)( 45, 91)( 46,125)( 47,124)( 48,123)( 49,122)( 50,121)( 51,101)( 52,105)( 53,104)( 54,103)( 55,102)( 66, 70)( 67, 69)( 71,100)( 72, 99)( 73, 98)( 74, 97)( 75, 96)( 77, 80)( 78, 79)( 81,108)( 82,107)( 83,106)( 84,110)( 85,109)(112,115)(113,114);;
s2 := (  1,  2)(  3,  5)(  6, 61)(  7, 65)(  8, 64)(  9, 63)( 10, 62)( 11,124)( 12,123)( 13,122)( 14,121)( 15,125)( 16, 31)( 17, 35)( 18, 34)( 19, 33)( 20, 32)( 21, 92)( 22, 91)( 23, 95)( 24, 94)( 25, 93)( 26, 85)( 27, 84)( 28, 83)( 29, 82)( 30, 81)( 36, 51)( 37, 55)( 38, 54)( 39, 53)( 40, 52)( 41,115)( 42,114)( 43,113)( 44,112)( 45,111)( 46, 48)( 49, 50)( 56, 99)( 57, 98)( 58, 97)( 59, 96)( 60,100)( 66, 67)( 68, 70)( 71,102)( 72,101)( 73,105)( 74,104)( 75,103)( 76,120)( 77,119)( 78,118)( 79,117)( 80,116)( 86, 89)( 87, 88)(106,109)(107,108);;
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, s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1, 
s0*s1*s2*s1*s2*s1*s2*s1*s0*s1*s2*s1*s2*s1*s2*s1, 
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1, 
s1*s2*s1*s0*s1*s0*s1*s0*s1*s2*s1*s0*s1*s2*s1*s2*s0*s1*s0*s1*s0 ];;
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, 58)(  7, 57)(  8, 56)(  9, 60)( 10, 59)( 11, 86)( 12, 90)( 13, 89)( 14, 88)( 15, 87)( 16,120)( 17,119)( 18,118)( 19,117)( 20,116)( 21, 25)( 22, 24)( 31, 33)( 34, 35)( 36, 61)( 37, 65)( 38, 64)( 39, 63)( 40, 62)( 41, 95)( 42, 94)( 43, 93)( 44, 92)( 45, 91)( 46,125)( 47,124)( 48,123)( 49,122)( 50,121)( 51,101)( 52,105)( 53,104)( 54,103)( 55,102)( 66, 70)( 67, 69)( 71,100)( 72, 99)( 73, 98)( 74, 97)( 75, 96)( 77, 80)( 78, 79)( 81,108)( 82,107)( 83,106)( 84,110)( 85,109)(112,115)(113,114);
s2 := Sym(125)!(  1,  2)(  3,  5)(  6, 61)(  7, 65)(  8, 64)(  9, 63)( 10, 62)( 11,124)( 12,123)( 13,122)( 14,121)( 15,125)( 16, 31)( 17, 35)( 18, 34)( 19, 33)( 20, 32)( 21, 92)( 22, 91)( 23, 95)( 24, 94)( 25, 93)( 26, 85)( 27, 84)( 28, 83)( 29, 82)( 30, 81)( 36, 51)( 37, 55)( 38, 54)( 39, 53)( 40, 52)( 41,115)( 42,114)( 43,113)( 44,112)( 45,111)( 46, 48)( 49, 50)( 56, 99)( 57, 98)( 58, 97)( 59, 96)( 60,100)( 66, 67)( 68, 70)( 71,102)( 72,101)( 73,105)( 74,104)( 75,103)( 76,120)( 77,119)( 78,118)( 79,117)( 80,116)( 86, 89)( 87, 88)(106,109)(107,108);
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, s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1, 
s0*s1*s2*s1*s2*s1*s2*s1*s0*s1*s2*s1*s2*s1*s2*s1, 
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1, 
s1*s2*s1*s0*s1*s0*s1*s0*s1*s2*s1*s0*s1*s2*s1*s2*s0*s1*s0*s1*s0 >;

References : None.
to this polytope

Polytope of Type {10,20}

Twisty Puzzle