Polytope of Type {20,10}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {20,10}*1000e
if this polytope has a name.
Group : SmallGroup(1000,179)
Rank : 3
Schlafli Type : {20,10}
Number of vertices, edges, etc : 50, 250, 25
Order of s₀s₁s₂ : 20
Order of s₀s₁s₂s₁ : 10
Special Properties :
   Compact Hyperbolic Quotient
   Locally Spherical
   Non-Orientable
   Self-Petrie
Related Polytopes :
   Facet
   Vertex Figure
   Dual
   Petrial
Facet Of :
   {20,10,2} of size 2000
Vertex Figure Of :
   {2,20,10} of size 2000
Quotients (Maximal Quotients in Boldface) :
   5-fold quotients : {4,10}*200
Covers (Minimal Covers in Boldface) :
   2-fold covers : {20,10}*2000j
Permutation Representation (GAP) :

s0 := (  2,  5)(  3,  4)(  6, 56)(  7, 60)(  8, 59)(  9, 58)( 10, 57)( 11,111)
( 12,115)( 13,114)( 14,113)( 15,112)( 16, 41)( 17, 45)( 18, 44)( 19, 43)
( 20, 42)( 21, 96)( 22,100)( 23, 99)( 24, 98)( 25, 97)( 26,101)( 27,105)
( 28,104)( 29,103)( 30,102)( 32, 35)( 33, 34)( 36, 86)( 37, 90)( 38, 89)
( 39, 88)( 40, 87)( 46, 71)( 47, 75)( 48, 74)( 49, 73)( 50, 72)( 51, 76)
( 52, 80)( 53, 79)( 54, 78)( 55, 77)( 62, 65)( 63, 64)( 66,116)( 67,120)
( 68,119)( 69,118)( 70,117)( 81,106)( 82,110)( 83,109)( 84,108)( 85,107)
( 92, 95)( 93, 94)(122,125)(123,124);;
s1 := (  1,  2)(  3,  5)(  6, 42)(  7, 41)(  8, 45)(  9, 44)( 10, 43)( 11, 57)
( 12, 56)( 13, 60)( 14, 59)( 15, 58)( 16, 97)( 17, 96)( 18,100)( 19, 99)
( 20, 98)( 21,112)( 22,111)( 23,115)( 24,114)( 25,113)( 26, 62)( 27, 61)
( 28, 65)( 29, 64)( 30, 63)( 31, 77)( 32, 76)( 33, 80)( 34, 79)( 35, 78)
( 36,117)( 37,116)( 38,120)( 39,119)( 40,118)( 46, 47)( 48, 50)( 51,122)
( 52,121)( 53,125)( 54,124)( 55,123)( 66, 67)( 68, 70)( 71, 82)( 72, 81)
( 73, 85)( 74, 84)( 75, 83)( 86, 87)( 88, 90)( 91,102)( 92,101)( 93,105)
( 94,104)( 95,103)(106,107)(108,110);;
s2 := (  1, 31)(  2, 32)(  3, 33)(  4, 34)(  5, 35)(  6, 26)(  7, 27)(  8, 28)
(  9, 29)( 10, 30)( 11, 46)( 12, 47)( 13, 48)( 14, 49)( 15, 50)( 16, 41)
( 17, 42)( 18, 43)( 19, 44)( 20, 45)( 21, 36)( 22, 37)( 23, 38)( 24, 39)
( 25, 40)( 51,106)( 52,107)( 53,108)( 54,109)( 55,110)( 56,101)( 57,102)
( 58,103)( 59,104)( 60,105)( 61,121)( 62,122)( 63,123)( 64,124)( 65,125)
( 66,116)( 67,117)( 68,118)( 69,119)( 70,120)( 71,111)( 72,112)( 73,113)
( 74,114)( 75,115)( 76, 81)( 77, 82)( 78, 83)( 79, 84)( 80, 85)( 86, 96)
( 87, 97)( 88, 98)( 89, 99)( 90,100);;
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*s0*s1*s2*s0*s1*s2*s1*s0*s1, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, 
s0*s1*s0*s1*s2*s0*s1*s0*s1*s2*s0*s1*s0*s1*s2*s0*s1*s0*s1*s2*s0*s1*s0*s1*s2 ];;
poly := F / rels;;

Permutation Representation (Magma) :

s0 := Sym(125)!(  2,  5)(  3,  4)(  6, 56)(  7, 60)(  8, 59)(  9, 58)( 10, 57)
( 11,111)( 12,115)( 13,114)( 14,113)( 15,112)( 16, 41)( 17, 45)( 18, 44)
( 19, 43)( 20, 42)( 21, 96)( 22,100)( 23, 99)( 24, 98)( 25, 97)( 26,101)
( 27,105)( 28,104)( 29,103)( 30,102)( 32, 35)( 33, 34)( 36, 86)( 37, 90)
( 38, 89)( 39, 88)( 40, 87)( 46, 71)( 47, 75)( 48, 74)( 49, 73)( 50, 72)
( 51, 76)( 52, 80)( 53, 79)( 54, 78)( 55, 77)( 62, 65)( 63, 64)( 66,116)
( 67,120)( 68,119)( 69,118)( 70,117)( 81,106)( 82,110)( 83,109)( 84,108)
( 85,107)( 92, 95)( 93, 94)(122,125)(123,124);
s1 := Sym(125)!(  1,  2)(  3,  5)(  6, 42)(  7, 41)(  8, 45)(  9, 44)( 10, 43)
( 11, 57)( 12, 56)( 13, 60)( 14, 59)( 15, 58)( 16, 97)( 17, 96)( 18,100)
( 19, 99)( 20, 98)( 21,112)( 22,111)( 23,115)( 24,114)( 25,113)( 26, 62)
( 27, 61)( 28, 65)( 29, 64)( 30, 63)( 31, 77)( 32, 76)( 33, 80)( 34, 79)
( 35, 78)( 36,117)( 37,116)( 38,120)( 39,119)( 40,118)( 46, 47)( 48, 50)
( 51,122)( 52,121)( 53,125)( 54,124)( 55,123)( 66, 67)( 68, 70)( 71, 82)
( 72, 81)( 73, 85)( 74, 84)( 75, 83)( 86, 87)( 88, 90)( 91,102)( 92,101)
( 93,105)( 94,104)( 95,103)(106,107)(108,110);
s2 := Sym(125)!(  1, 31)(  2, 32)(  3, 33)(  4, 34)(  5, 35)(  6, 26)(  7, 27)
(  8, 28)(  9, 29)( 10, 30)( 11, 46)( 12, 47)( 13, 48)( 14, 49)( 15, 50)
( 16, 41)( 17, 42)( 18, 43)( 19, 44)( 20, 45)( 21, 36)( 22, 37)( 23, 38)
( 24, 39)( 25, 40)( 51,106)( 52,107)( 53,108)( 54,109)( 55,110)( 56,101)
( 57,102)( 58,103)( 59,104)( 60,105)( 61,121)( 62,122)( 63,123)( 64,124)
( 65,125)( 66,116)( 67,117)( 68,118)( 69,119)( 70,120)( 71,111)( 72,112)
( 73,113)( 74,114)( 75,115)( 76, 81)( 77, 82)( 78, 83)( 79, 84)( 80, 85)
( 86, 96)( 87, 97)( 88, 98)( 89, 99)( 90,100);
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*s0*s1*s2*s0*s1*s2*s1*s0*s1, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, 
s0*s1*s0*s1*s2*s0*s1*s0*s1*s2*s0*s1*s0*s1*s2*s0*s1*s0*s1*s2*s0*s1*s0*s1*s2 >;

References : None.
to this polytope