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Polytope of Type {4,20}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {4,20}*800
if this polytope has a name.
Group : SmallGroup(800,1058)
Rank : 3
Schlafli Type : {4,20}
Number of vertices, edges, etc : 20, 200, 100
Order of s0s1s2 : 4
Order of s0s1s2s1 : 10
Special Properties :
   Compact Hyperbolic Quotient
   Locally Spherical
   Orientable
   Self-Petrie
Related Polytopes :
   Facet
   Vertex Figure
   Dual
   Petrial
Facet Of :
   {4,20,2} of size 1600
Vertex Figure Of :
   {2,4,20} of size 1600
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {4,10}*400
   4-fold quotients : {4,10}*200
   25-fold quotients : {4,4}*32
   50-fold quotients : {2,4}*16, {4,2}*16
   100-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
   2-fold covers : {4,20}*1600, {8,20}*1600a, {4,40}*1600a, {4,40}*1600b, {8,20}*1600b
Permutation Representation (GAP) :
s0 := (  2,  7)(  3, 13)(  4, 19)(  5, 25)(  6, 21)(  9, 14)( 10, 20)( 11, 16)
( 12, 22)( 18, 23)( 27, 32)( 28, 38)( 29, 44)( 30, 50)( 31, 46)( 34, 39)
( 35, 45)( 36, 41)( 37, 47)( 43, 48)( 52, 57)( 53, 63)( 54, 69)( 55, 75)
( 56, 71)( 59, 64)( 60, 70)( 61, 66)( 62, 72)( 68, 73)( 77, 82)( 78, 88)
( 79, 94)( 80,100)( 81, 96)( 84, 89)( 85, 95)( 86, 91)( 87, 97)( 93, 98);;
s1 := (  2, 19)(  3,  7)(  4, 25)(  5, 13)(  6, 15)(  8, 16)( 10, 22)( 11, 24)
( 14, 18)( 17, 21)( 27, 44)( 28, 32)( 29, 50)( 30, 38)( 31, 40)( 33, 41)
( 35, 47)( 36, 49)( 39, 43)( 42, 46)( 51, 76)( 52, 94)( 53, 82)( 54,100)
( 55, 88)( 56, 90)( 57, 78)( 58, 91)( 59, 84)( 60, 97)( 61, 99)( 62, 87)
( 63, 80)( 64, 93)( 65, 81)( 66, 83)( 67, 96)( 68, 89)( 69, 77)( 70, 95)
( 71, 92)( 72, 85)( 73, 98)( 74, 86)( 75, 79);;
s2 := (  1, 58)(  2, 57)(  3, 56)(  4, 60)(  5, 59)(  6, 53)(  7, 52)(  8, 51)
(  9, 55)( 10, 54)( 11, 73)( 12, 72)( 13, 71)( 14, 75)( 15, 74)( 16, 68)
( 17, 67)( 18, 66)( 19, 70)( 20, 69)( 21, 63)( 22, 62)( 23, 61)( 24, 65)
( 25, 64)( 26, 83)( 27, 82)( 28, 81)( 29, 85)( 30, 84)( 31, 78)( 32, 77)
( 33, 76)( 34, 80)( 35, 79)( 36, 98)( 37, 97)( 38, 96)( 39,100)( 40, 99)
( 41, 93)( 42, 92)( 43, 91)( 44, 95)( 45, 94)( 46, 88)( 47, 87)( 48, 86)
( 49, 90)( 50, 89);;
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*s0*s1*s0*s1*s0*s1, 
s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1, 
s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1 ];;
poly := F / rels;;
 
Permutation Representation (Magma) :
s0 := Sym(100)!(  2,  7)(  3, 13)(  4, 19)(  5, 25)(  6, 21)(  9, 14)( 10, 20)
( 11, 16)( 12, 22)( 18, 23)( 27, 32)( 28, 38)( 29, 44)( 30, 50)( 31, 46)
( 34, 39)( 35, 45)( 36, 41)( 37, 47)( 43, 48)( 52, 57)( 53, 63)( 54, 69)
( 55, 75)( 56, 71)( 59, 64)( 60, 70)( 61, 66)( 62, 72)( 68, 73)( 77, 82)
( 78, 88)( 79, 94)( 80,100)( 81, 96)( 84, 89)( 85, 95)( 86, 91)( 87, 97)
( 93, 98);
s1 := Sym(100)!(  2, 19)(  3,  7)(  4, 25)(  5, 13)(  6, 15)(  8, 16)( 10, 22)
( 11, 24)( 14, 18)( 17, 21)( 27, 44)( 28, 32)( 29, 50)( 30, 38)( 31, 40)
( 33, 41)( 35, 47)( 36, 49)( 39, 43)( 42, 46)( 51, 76)( 52, 94)( 53, 82)
( 54,100)( 55, 88)( 56, 90)( 57, 78)( 58, 91)( 59, 84)( 60, 97)( 61, 99)
( 62, 87)( 63, 80)( 64, 93)( 65, 81)( 66, 83)( 67, 96)( 68, 89)( 69, 77)
( 70, 95)( 71, 92)( 72, 85)( 73, 98)( 74, 86)( 75, 79);
s2 := Sym(100)!(  1, 58)(  2, 57)(  3, 56)(  4, 60)(  5, 59)(  6, 53)(  7, 52)
(  8, 51)(  9, 55)( 10, 54)( 11, 73)( 12, 72)( 13, 71)( 14, 75)( 15, 74)
( 16, 68)( 17, 67)( 18, 66)( 19, 70)( 20, 69)( 21, 63)( 22, 62)( 23, 61)
( 24, 65)( 25, 64)( 26, 83)( 27, 82)( 28, 81)( 29, 85)( 30, 84)( 31, 78)
( 32, 77)( 33, 76)( 34, 80)( 35, 79)( 36, 98)( 37, 97)( 38, 96)( 39,100)
( 40, 99)( 41, 93)( 42, 92)( 43, 91)( 44, 95)( 45, 94)( 46, 88)( 47, 87)
( 48, 86)( 49, 90)( 50, 89);
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, s0*s1*s0*s1*s0*s1*s0*s1, 
s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1, 
s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1 >; 
 
References : None.
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