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Polytope of Type {20,10,2,2}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {20,10,2,2}*1600a
if this polytope has a name.
Group : SmallGroup(1600,10161)
Rank : 5
Schlafli Type : {20,10,2,2}
Number of vertices, edges, etc : 20, 100, 10, 2, 2
Order of s0s1s2s3s4 : 20
Order of s0s1s2s3s4s3s2s1 : 2
Special Properties :
   Degenerate
   Universal
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   None in this Atlas
Vertex Figure Of :
   None in this Atlas
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {10,10,2,2}*800a
   5-fold quotients : {20,2,2,2}*320, {4,10,2,2}*320
   10-fold quotients : {2,10,2,2}*160, {10,2,2,2}*160
   20-fold quotients : {2,5,2,2}*80, {5,2,2,2}*80
   25-fold quotients : {4,2,2,2}*64
   50-fold quotients : {2,2,2,2}*32
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :
s0 := (  6, 21)(  7, 22)(  8, 23)(  9, 24)( 10, 25)( 11, 16)( 12, 17)( 13, 18)
( 14, 19)( 15, 20)( 31, 46)( 32, 47)( 33, 48)( 34, 49)( 35, 50)( 36, 41)
( 37, 42)( 38, 43)( 39, 44)( 40, 45)( 51, 76)( 52, 77)( 53, 78)( 54, 79)
( 55, 80)( 56, 96)( 57, 97)( 58, 98)( 59, 99)( 60,100)( 61, 91)( 62, 92)
( 63, 93)( 64, 94)( 65, 95)( 66, 86)( 67, 87)( 68, 88)( 69, 89)( 70, 90)
( 71, 81)( 72, 82)( 73, 83)( 74, 84)( 75, 85);;
s1 := (  1, 56)(  2, 60)(  3, 59)(  4, 58)(  5, 57)(  6, 51)(  7, 55)(  8, 54)
(  9, 53)( 10, 52)( 11, 71)( 12, 75)( 13, 74)( 14, 73)( 15, 72)( 16, 66)
( 17, 70)( 18, 69)( 19, 68)( 20, 67)( 21, 61)( 22, 65)( 23, 64)( 24, 63)
( 25, 62)( 26, 81)( 27, 85)( 28, 84)( 29, 83)( 30, 82)( 31, 76)( 32, 80)
( 33, 79)( 34, 78)( 35, 77)( 36, 96)( 37,100)( 38, 99)( 39, 98)( 40, 97)
( 41, 91)( 42, 95)( 43, 94)( 44, 93)( 45, 92)( 46, 86)( 47, 90)( 48, 89)
( 49, 88)( 50, 87);;
s2 := (  1,  2)(  3,  5)(  6,  7)(  8, 10)( 11, 12)( 13, 15)( 16, 17)( 18, 20)
( 21, 22)( 23, 25)( 26, 27)( 28, 30)( 31, 32)( 33, 35)( 36, 37)( 38, 40)
( 41, 42)( 43, 45)( 46, 47)( 48, 50)( 51, 52)( 53, 55)( 56, 57)( 58, 60)
( 61, 62)( 63, 65)( 66, 67)( 68, 70)( 71, 72)( 73, 75)( 76, 77)( 78, 80)
( 81, 82)( 83, 85)( 86, 87)( 88, 90)( 91, 92)( 93, 95)( 96, 97)( 98,100);;
s3 := (101,102);;
s4 := (103,104);;
poly := Group([s0,s1,s2,s3,s4]);;
 
Finitely Presented Group Representation (GAP) :
F := FreeGroup("s0","s1","s2","s3","s4");;
s0 := F.1;;  s1 := F.2;;  s2 := F.3;;  s3 := F.4;;  s4 := F.5;;  
rels := [ s0*s0, s1*s1, s2*s2, s3*s3, s4*s4, s0*s2*s0*s2, 
s0*s3*s0*s3, s1*s3*s1*s3, s2*s3*s2*s3, 
s0*s4*s0*s4, s1*s4*s1*s4, s2*s4*s2*s4, 
s3*s4*s3*s4, s0*s1*s2*s1*s0*s1*s2*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*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 ];;
poly := F / rels;;
 
Permutation Representation (Magma) :
s0 := Sym(104)!(  6, 21)(  7, 22)(  8, 23)(  9, 24)( 10, 25)( 11, 16)( 12, 17)
( 13, 18)( 14, 19)( 15, 20)( 31, 46)( 32, 47)( 33, 48)( 34, 49)( 35, 50)
( 36, 41)( 37, 42)( 38, 43)( 39, 44)( 40, 45)( 51, 76)( 52, 77)( 53, 78)
( 54, 79)( 55, 80)( 56, 96)( 57, 97)( 58, 98)( 59, 99)( 60,100)( 61, 91)
( 62, 92)( 63, 93)( 64, 94)( 65, 95)( 66, 86)( 67, 87)( 68, 88)( 69, 89)
( 70, 90)( 71, 81)( 72, 82)( 73, 83)( 74, 84)( 75, 85);
s1 := Sym(104)!(  1, 56)(  2, 60)(  3, 59)(  4, 58)(  5, 57)(  6, 51)(  7, 55)
(  8, 54)(  9, 53)( 10, 52)( 11, 71)( 12, 75)( 13, 74)( 14, 73)( 15, 72)
( 16, 66)( 17, 70)( 18, 69)( 19, 68)( 20, 67)( 21, 61)( 22, 65)( 23, 64)
( 24, 63)( 25, 62)( 26, 81)( 27, 85)( 28, 84)( 29, 83)( 30, 82)( 31, 76)
( 32, 80)( 33, 79)( 34, 78)( 35, 77)( 36, 96)( 37,100)( 38, 99)( 39, 98)
( 40, 97)( 41, 91)( 42, 95)( 43, 94)( 44, 93)( 45, 92)( 46, 86)( 47, 90)
( 48, 89)( 49, 88)( 50, 87);
s2 := Sym(104)!(  1,  2)(  3,  5)(  6,  7)(  8, 10)( 11, 12)( 13, 15)( 16, 17)
( 18, 20)( 21, 22)( 23, 25)( 26, 27)( 28, 30)( 31, 32)( 33, 35)( 36, 37)
( 38, 40)( 41, 42)( 43, 45)( 46, 47)( 48, 50)( 51, 52)( 53, 55)( 56, 57)
( 58, 60)( 61, 62)( 63, 65)( 66, 67)( 68, 70)( 71, 72)( 73, 75)( 76, 77)
( 78, 80)( 81, 82)( 83, 85)( 86, 87)( 88, 90)( 91, 92)( 93, 95)( 96, 97)
( 98,100);
s3 := Sym(104)!(101,102);
s4 := Sym(104)!(103,104);
poly := sub<Sym(104)|s0,s1,s2,s3,s4>;
 
Finitely Presented Group Representation (Magma) :
poly<s0,s1,s2,s3,s4> := Group< s0,s1,s2,s3,s4 | s0*s0, s1*s1, s2*s2, 
s3*s3, s4*s4, s0*s2*s0*s2, s0*s3*s0*s3, 
s1*s3*s1*s3, s2*s3*s2*s3, s0*s4*s0*s4, 
s1*s4*s1*s4, s2*s4*s2*s4, s3*s4*s3*s4, 
s0*s1*s2*s1*s0*s1*s2*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*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 >; 
 

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