Polytope of Type {6,3}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {6,3}*1200
Also Known As : {6,3}_(10,0), {6,3}₂₀. if this polytope has another name.
Group : SmallGroup(1200,985)
Rank : 3
Schlafli Type : {6,3}
Number of vertices, edges, etc : 200, 300, 100
Order of s₀s₁s₂ : 20
Order of s₀s₁s₂s₁ : 6
Special Properties :
   Toroidal
   Locally Spherical
   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) :
   4-fold quotients : {6,3}*300
   25-fold quotients : {6,3}*48
   50-fold quotients : {3,3}*24
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

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

Permutation Representation (Magma) :

s0 := Sym(100)!(  6, 25)(  7, 21)(  8, 22)(  9, 23)( 10, 24)( 11, 19)( 12, 20)
( 13, 16)( 14, 17)( 15, 18)( 31, 50)( 32, 46)( 33, 47)( 34, 48)( 35, 49)
( 36, 44)( 37, 45)( 38, 41)( 39, 42)( 40, 43)( 51, 76)( 52, 77)( 53, 78)
( 54, 79)( 55, 80)( 56,100)( 57, 96)( 58, 97)( 59, 98)( 60, 99)( 61, 94)
( 62, 95)( 63, 91)( 64, 92)( 65, 93)( 66, 88)( 67, 89)( 68, 90)( 69, 86)
( 70, 87)( 71, 82)( 72, 83)( 73, 84)( 74, 85)( 75, 81);
s1 := Sym(100)!(  2,  7)(  3, 13)(  4, 19)(  5, 25)(  6, 21)(  9, 14)( 10, 20)
( 11, 16)( 12, 22)( 18, 23)( 26, 76)( 27, 82)( 28, 88)( 29, 94)( 30,100)
( 31, 96)( 32, 77)( 33, 83)( 34, 89)( 35, 95)( 36, 91)( 37, 97)( 38, 78)
( 39, 84)( 40, 90)( 41, 86)( 42, 92)( 43, 98)( 44, 79)( 45, 85)( 46, 81)
( 47, 87)( 48, 93)( 49, 99)( 50, 80)( 52, 57)( 53, 63)( 54, 69)( 55, 75)
( 56, 71)( 59, 64)( 60, 70)( 61, 66)( 62, 72)( 68, 73);
s2 := Sym(100)!(  1, 27)(  2, 26)(  3, 30)(  4, 29)(  5, 28)(  6, 33)(  7, 32)
(  8, 31)(  9, 35)( 10, 34)( 11, 39)( 12, 38)( 13, 37)( 14, 36)( 15, 40)
( 16, 45)( 17, 44)( 18, 43)( 19, 42)( 20, 41)( 21, 46)( 22, 50)( 23, 49)
( 24, 48)( 25, 47)( 51, 52)( 53, 55)( 56, 58)( 59, 60)( 61, 64)( 62, 63)
( 66, 70)( 67, 69)( 72, 75)( 73, 74)( 76, 77)( 78, 80)( 81, 83)( 84, 85)
( 86, 89)( 87, 88)( 91, 95)( 92, 94)( 97,100)( 98, 99);
poly := sub<Sym(100)|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, s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1, 
s0*s2*s1*s0*s2*s1*s0*s2*s1*s0*s2*s1*s0*s2*s1*s0*s2*s1*s0*s2*s1*s0*s2*s1*s0*s2*s1*s0*s2*s1*s0*s2*s1*s0*s2*s1*s0*s2*s1*s0*s2*s1*s0*s2*s1*s0*s2*s1*s0*s2*s1*s0*s2*s1*s0*s2*s1*s0*s2*s1 >;

References : None.
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