Polytope of Type {10,4}

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

References : None.
to this polytope