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Polytope of Type {2,10,20}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,10,20}*800c
if this polytope has a name.
Group : SmallGroup(800,1153)
Rank : 4
Schlafli Type : {2,10,20}
Number of vertices, edges, etc : 2, 10, 100, 20
Order of s0s1s2s3 : 20
Order of s0s1s2s3s2s1 : 2
Special Properties :
   Degenerate
   Universal
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {2,10,20,2} of size 1600
Vertex Figure Of :
   {2,2,10,20} of size 1600
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {2,10,10}*400c
   4-fold quotients : {2,5,10}*200
   5-fold quotients : {2,10,4}*160
   10-fold quotients : {2,10,2}*80
   20-fold quotients : {2,5,2}*40
   25-fold quotients : {2,2,4}*32
   50-fold quotients : {2,2,2}*16
Covers (Minimal Covers in Boldface) :
   2-fold covers : {2,20,20}*1600c, {4,10,20}*1600c, {2,10,40}*1600c
Permutation Representation (GAP) :
s0 := (1,2);;
s1 := (  4,  7)(  5,  6)(  8, 23)(  9, 27)( 10, 26)( 11, 25)( 12, 24)( 13, 18)
( 14, 22)( 15, 21)( 16, 20)( 17, 19)( 29, 32)( 30, 31)( 33, 48)( 34, 52)
( 35, 51)( 36, 50)( 37, 49)( 38, 43)( 39, 47)( 40, 46)( 41, 45)( 42, 44)
( 54, 57)( 55, 56)( 58, 73)( 59, 77)( 60, 76)( 61, 75)( 62, 74)( 63, 68)
( 64, 72)( 65, 71)( 66, 70)( 67, 69)( 79, 82)( 80, 81)( 83, 98)( 84,102)
( 85,101)( 86,100)( 87, 99)( 88, 93)( 89, 97)( 90, 96)( 91, 95)( 92, 94);;
s2 := (  3, 59)(  4, 58)(  5, 62)(  6, 61)(  7, 60)(  8, 54)(  9, 53)( 10, 57)
( 11, 56)( 12, 55)( 13, 74)( 14, 73)( 15, 77)( 16, 76)( 17, 75)( 18, 69)
( 19, 68)( 20, 72)( 21, 71)( 22, 70)( 23, 64)( 24, 63)( 25, 67)( 26, 66)
( 27, 65)( 28, 84)( 29, 83)( 30, 87)( 31, 86)( 32, 85)( 33, 79)( 34, 78)
( 35, 82)( 36, 81)( 37, 80)( 38, 99)( 39, 98)( 40,102)( 41,101)( 42,100)
( 43, 94)( 44, 93)( 45, 97)( 46, 96)( 47, 95)( 48, 89)( 49, 88)( 50, 92)
( 51, 91)( 52, 90);;
s3 := (  4,  7)(  5,  6)(  9, 12)( 10, 11)( 14, 17)( 15, 16)( 19, 22)( 20, 21)
( 24, 27)( 25, 26)( 29, 32)( 30, 31)( 34, 37)( 35, 36)( 39, 42)( 40, 41)
( 44, 47)( 45, 46)( 49, 52)( 50, 51)( 53, 78)( 54, 82)( 55, 81)( 56, 80)
( 57, 79)( 58, 83)( 59, 87)( 60, 86)( 61, 85)( 62, 84)( 63, 88)( 64, 92)
( 65, 91)( 66, 90)( 67, 89)( 68, 93)( 69, 97)( 70, 96)( 71, 95)( 72, 94)
( 73, 98)( 74,102)( 75,101)( 76,100)( 77, 99);;
poly := Group([s0,s1,s2,s3]);;
 
Finitely Presented Group Representation (GAP) :
F := FreeGroup("s0","s1","s2","s3");;
s0 := F.1;;  s1 := F.2;;  s2 := F.3;;  s3 := F.4;;  
rels := [ s0*s0, s1*s1, s2*s2, s3*s3, s0*s1*s0*s1, 
s0*s2*s0*s2, s0*s3*s0*s3, s1*s3*s1*s3, 
s3*s1*s2*s3*s2*s3*s1*s2*s3*s2, s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 ];;
poly := F / rels;;
 
Permutation Representation (Magma) :
s0 := Sym(102)!(1,2);
s1 := Sym(102)!(  4,  7)(  5,  6)(  8, 23)(  9, 27)( 10, 26)( 11, 25)( 12, 24)
( 13, 18)( 14, 22)( 15, 21)( 16, 20)( 17, 19)( 29, 32)( 30, 31)( 33, 48)
( 34, 52)( 35, 51)( 36, 50)( 37, 49)( 38, 43)( 39, 47)( 40, 46)( 41, 45)
( 42, 44)( 54, 57)( 55, 56)( 58, 73)( 59, 77)( 60, 76)( 61, 75)( 62, 74)
( 63, 68)( 64, 72)( 65, 71)( 66, 70)( 67, 69)( 79, 82)( 80, 81)( 83, 98)
( 84,102)( 85,101)( 86,100)( 87, 99)( 88, 93)( 89, 97)( 90, 96)( 91, 95)
( 92, 94);
s2 := Sym(102)!(  3, 59)(  4, 58)(  5, 62)(  6, 61)(  7, 60)(  8, 54)(  9, 53)
( 10, 57)( 11, 56)( 12, 55)( 13, 74)( 14, 73)( 15, 77)( 16, 76)( 17, 75)
( 18, 69)( 19, 68)( 20, 72)( 21, 71)( 22, 70)( 23, 64)( 24, 63)( 25, 67)
( 26, 66)( 27, 65)( 28, 84)( 29, 83)( 30, 87)( 31, 86)( 32, 85)( 33, 79)
( 34, 78)( 35, 82)( 36, 81)( 37, 80)( 38, 99)( 39, 98)( 40,102)( 41,101)
( 42,100)( 43, 94)( 44, 93)( 45, 97)( 46, 96)( 47, 95)( 48, 89)( 49, 88)
( 50, 92)( 51, 91)( 52, 90);
s3 := Sym(102)!(  4,  7)(  5,  6)(  9, 12)( 10, 11)( 14, 17)( 15, 16)( 19, 22)
( 20, 21)( 24, 27)( 25, 26)( 29, 32)( 30, 31)( 34, 37)( 35, 36)( 39, 42)
( 40, 41)( 44, 47)( 45, 46)( 49, 52)( 50, 51)( 53, 78)( 54, 82)( 55, 81)
( 56, 80)( 57, 79)( 58, 83)( 59, 87)( 60, 86)( 61, 85)( 62, 84)( 63, 88)
( 64, 92)( 65, 91)( 66, 90)( 67, 89)( 68, 93)( 69, 97)( 70, 96)( 71, 95)
( 72, 94)( 73, 98)( 74,102)( 75,101)( 76,100)( 77, 99);
poly := sub<Sym(102)|s0,s1,s2,s3>;
 
Finitely Presented Group Representation (Magma) :
poly<s0,s1,s2,s3> := Group< s0,s1,s2,s3 | s0*s0, s1*s1, s2*s2, 
s3*s3, s0*s1*s0*s1, s0*s2*s0*s2, s0*s3*s0*s3, 
s1*s3*s1*s3, s3*s1*s2*s3*s2*s3*s1*s2*s3*s2, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 >; 
 

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