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Polytope of Type {2,16,14,2}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,16,14,2}*1792
if this polytope has a name.
Group : SmallGroup(1792,1076041)
Rank : 5
Schlafli Type : {2,16,14,2}
Number of vertices, edges, etc : 2, 16, 112, 14, 2
Order of s0s1s2s3s4 : 112
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 : {2,8,14,2}*896
   4-fold quotients : {2,4,14,2}*448
   7-fold quotients : {2,16,2,2}*256
   8-fold quotients : {2,2,14,2}*224
   14-fold quotients : {2,8,2,2}*128
   16-fold quotients : {2,2,7,2}*112
   28-fold quotients : {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, 45)
( 32, 46)( 33, 47)( 34, 48)( 35, 49)( 36, 50)( 37, 51)( 38, 52)( 39, 53)
( 40, 54)( 41, 55)( 42, 56)( 43, 57)( 44, 58)( 59, 87)( 60, 88)( 61, 89)
( 62, 90)( 63, 91)( 64, 92)( 65, 93)( 66, 94)( 67, 95)( 68, 96)( 69, 97)
( 70, 98)( 71, 99)( 72,100)( 73,108)( 74,109)( 75,110)( 76,111)( 77,112)
( 78,113)( 79,114)( 80,101)( 81,102)( 82,103)( 83,104)( 84,105)( 85,106)
( 86,107);;
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)( 31,101)( 32,107)( 33,106)( 34,105)
( 35,104)( 36,103)( 37,102)( 38,108)( 39,114)( 40,113)( 41,112)( 42,111)
( 43,110)( 44,109)( 45, 87)( 46, 93)( 47, 92)( 48, 91)( 49, 90)( 50, 89)
( 51, 88)( 52, 94)( 53,100)( 54, 99)( 55, 98)( 56, 97)( 57, 96)( 58, 95);;
s3 := (  3,  4)(  5,  9)(  6,  8)( 10, 11)( 12, 16)( 13, 15)( 17, 18)( 19, 23)
( 20, 22)( 24, 25)( 26, 30)( 27, 29)( 31, 32)( 33, 37)( 34, 36)( 38, 39)
( 40, 44)( 41, 43)( 45, 46)( 47, 51)( 48, 50)( 52, 53)( 54, 58)( 55, 57)
( 59, 60)( 61, 65)( 62, 64)( 66, 67)( 68, 72)( 69, 71)( 73, 74)( 75, 79)
( 76, 78)( 80, 81)( 82, 86)( 83, 85)( 87, 88)( 89, 93)( 90, 92)( 94, 95)
( 96,100)( 97, 99)(101,102)(103,107)(104,106)(108,109)(110,114)(111,113);;
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, s1*s2*s3*s2*s1*s2*s3*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, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*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(116)!(1,2);
s1 := Sym(116)!( 17, 24)( 18, 25)( 19, 26)( 20, 27)( 21, 28)( 22, 29)( 23, 30)
( 31, 45)( 32, 46)( 33, 47)( 34, 48)( 35, 49)( 36, 50)( 37, 51)( 38, 52)
( 39, 53)( 40, 54)( 41, 55)( 42, 56)( 43, 57)( 44, 58)( 59, 87)( 60, 88)
( 61, 89)( 62, 90)( 63, 91)( 64, 92)( 65, 93)( 66, 94)( 67, 95)( 68, 96)
( 69, 97)( 70, 98)( 71, 99)( 72,100)( 73,108)( 74,109)( 75,110)( 76,111)
( 77,112)( 78,113)( 79,114)( 80,101)( 81,102)( 82,103)( 83,104)( 84,105)
( 85,106)( 86,107);
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)( 31,101)( 32,107)( 33,106)
( 34,105)( 35,104)( 36,103)( 37,102)( 38,108)( 39,114)( 40,113)( 41,112)
( 42,111)( 43,110)( 44,109)( 45, 87)( 46, 93)( 47, 92)( 48, 91)( 49, 90)
( 50, 89)( 51, 88)( 52, 94)( 53,100)( 54, 99)( 55, 98)( 56, 97)( 57, 96)
( 58, 95);
s3 := Sym(116)!(  3,  4)(  5,  9)(  6,  8)( 10, 11)( 12, 16)( 13, 15)( 17, 18)
( 19, 23)( 20, 22)( 24, 25)( 26, 30)( 27, 29)( 31, 32)( 33, 37)( 34, 36)
( 38, 39)( 40, 44)( 41, 43)( 45, 46)( 47, 51)( 48, 50)( 52, 53)( 54, 58)
( 55, 57)( 59, 60)( 61, 65)( 62, 64)( 66, 67)( 68, 72)( 69, 71)( 73, 74)
( 75, 79)( 76, 78)( 80, 81)( 82, 86)( 83, 85)( 87, 88)( 89, 93)( 90, 92)
( 94, 95)( 96,100)( 97, 99)(101,102)(103,107)(104,106)(108,109)(110,114)
(111,113);
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, 
s1*s2*s3*s2*s1*s2*s3*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, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*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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