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Polytope of Type {2,8,28,2}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,8,28,2}*1792b
if this polytope has a name.
Group : SmallGroup(1792,1036171)
Rank : 5
Schlafli Type : {2,8,28,2}
Number of vertices, edges, etc : 2, 8, 112, 28, 2
Order of s0s1s2s3s4 : 56
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 : {2,4,28,2}*896
   4-fold quotients : {2,2,28,2}*448, {2,4,14,2}*448
   7-fold quotients : {2,8,4,2}*256b
   8-fold quotients : {2,2,14,2}*224
   14-fold quotients : {2,4,4,2}*128
   16-fold quotients : {2,2,7,2}*112
   28-fold quotients : {2,2,4,2}*64, {2,4,2,2}*64
   56-fold quotients : {2,2,2,2}*32
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :
s0 := (1,2);;
s1 := ( 17, 24)( 18, 25)( 19, 26)( 20, 27)( 21, 28)( 22, 29)( 23, 30)( 31, 38)
( 32, 39)( 33, 40)( 34, 41)( 35, 42)( 36, 43)( 37, 44)( 59, 73)( 60, 74)
( 61, 75)( 62, 76)( 63, 77)( 64, 78)( 65, 79)( 66, 80)( 67, 81)( 68, 82)
( 69, 83)( 70, 84)( 71, 85)( 72, 86)( 87,108)( 88,109)( 89,110)( 90,111)
( 91,112)( 92,113)( 93,114)( 94,101)( 95,102)( 96,103)( 97,104)( 98,105)
( 99,106)(100,107);;
s2 := (  3, 59)(  4, 65)(  5, 64)(  6, 63)(  7, 62)(  8, 61)(  9, 60)( 10, 66)
( 11, 72)( 12, 71)( 13, 70)( 14, 69)( 15, 68)( 16, 67)( 17, 80)( 18, 86)
( 19, 85)( 20, 84)( 21, 83)( 22, 82)( 23, 81)( 24, 73)( 25, 79)( 26, 78)
( 27, 77)( 28, 76)( 29, 75)( 30, 74)( 31, 87)( 32, 93)( 33, 92)( 34, 91)
( 35, 90)( 36, 89)( 37, 88)( 38, 94)( 39,100)( 40, 99)( 41, 98)( 42, 97)
( 43, 96)( 44, 95)( 45,108)( 46,114)( 47,113)( 48,112)( 49,111)( 50,110)
( 51,109)( 52,101)( 53,107)( 54,106)( 55,105)( 56,104)( 57,103)( 58,102);;
s3 := (  3,  4)(  5,  9)(  6,  8)( 10, 11)( 12, 16)( 13, 15)( 17, 25)( 18, 24)
( 19, 30)( 20, 29)( 21, 28)( 22, 27)( 23, 26)( 31, 32)( 33, 37)( 34, 36)
( 38, 39)( 40, 44)( 41, 43)( 45, 53)( 46, 52)( 47, 58)( 48, 57)( 49, 56)
( 50, 55)( 51, 54)( 59, 88)( 60, 87)( 61, 93)( 62, 92)( 63, 91)( 64, 90)
( 65, 89)( 66, 95)( 67, 94)( 68,100)( 69, 99)( 70, 98)( 71, 97)( 72, 96)
( 73,109)( 74,108)( 75,114)( 76,113)( 77,112)( 78,111)( 79,110)( 80,102)
( 81,101)( 82,107)( 83,106)( 84,105)( 85,104)( 86,103);;
s4 := (115,116);;
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*s1*s0*s1, 
s0*s2*s0*s2, s0*s3*s0*s3, s1*s3*s1*s3, 
s0*s4*s0*s4, s1*s4*s1*s4, s2*s4*s2*s4, 
s3*s4*s3*s4, s3*s1*s2*s1*s2*s3*s1*s2*s1*s2, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, 
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3 ];;
poly := F / rels;;
 
Permutation Representation (Magma) :
s0 := Sym(116)!(1,2);
s1 := Sym(116)!( 17, 24)( 18, 25)( 19, 26)( 20, 27)( 21, 28)( 22, 29)( 23, 30)
( 31, 38)( 32, 39)( 33, 40)( 34, 41)( 35, 42)( 36, 43)( 37, 44)( 59, 73)
( 60, 74)( 61, 75)( 62, 76)( 63, 77)( 64, 78)( 65, 79)( 66, 80)( 67, 81)
( 68, 82)( 69, 83)( 70, 84)( 71, 85)( 72, 86)( 87,108)( 88,109)( 89,110)
( 90,111)( 91,112)( 92,113)( 93,114)( 94,101)( 95,102)( 96,103)( 97,104)
( 98,105)( 99,106)(100,107);
s2 := Sym(116)!(  3, 59)(  4, 65)(  5, 64)(  6, 63)(  7, 62)(  8, 61)(  9, 60)
( 10, 66)( 11, 72)( 12, 71)( 13, 70)( 14, 69)( 15, 68)( 16, 67)( 17, 80)
( 18, 86)( 19, 85)( 20, 84)( 21, 83)( 22, 82)( 23, 81)( 24, 73)( 25, 79)
( 26, 78)( 27, 77)( 28, 76)( 29, 75)( 30, 74)( 31, 87)( 32, 93)( 33, 92)
( 34, 91)( 35, 90)( 36, 89)( 37, 88)( 38, 94)( 39,100)( 40, 99)( 41, 98)
( 42, 97)( 43, 96)( 44, 95)( 45,108)( 46,114)( 47,113)( 48,112)( 49,111)
( 50,110)( 51,109)( 52,101)( 53,107)( 54,106)( 55,105)( 56,104)( 57,103)
( 58,102);
s3 := Sym(116)!(  3,  4)(  5,  9)(  6,  8)( 10, 11)( 12, 16)( 13, 15)( 17, 25)
( 18, 24)( 19, 30)( 20, 29)( 21, 28)( 22, 27)( 23, 26)( 31, 32)( 33, 37)
( 34, 36)( 38, 39)( 40, 44)( 41, 43)( 45, 53)( 46, 52)( 47, 58)( 48, 57)
( 49, 56)( 50, 55)( 51, 54)( 59, 88)( 60, 87)( 61, 93)( 62, 92)( 63, 91)
( 64, 90)( 65, 89)( 66, 95)( 67, 94)( 68,100)( 69, 99)( 70, 98)( 71, 97)
( 72, 96)( 73,109)( 74,108)( 75,114)( 76,113)( 77,112)( 78,111)( 79,110)
( 80,102)( 81,101)( 82,107)( 83,106)( 84,105)( 85,104)( 86,103);
s4 := Sym(116)!(115,116);
poly := sub<Sym(116)|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*s1*s0*s1, s0*s2*s0*s2, 
s0*s3*s0*s3, s1*s3*s1*s3, s0*s4*s0*s4, 
s1*s4*s1*s4, s2*s4*s2*s4, s3*s4*s3*s4, 
s3*s1*s2*s1*s2*s3*s1*s2*s1*s2, s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, 
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3 >; 
 

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