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Polytope of Type {2,14,16}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,14,16}*896
if this polytope has a name.
Group : SmallGroup(896,14227)
Rank : 4
Schlafli Type : {2,14,16}
Number of vertices, edges, etc : 2, 14, 112, 16
Order of s0s1s2s3 : 112
Order of s0s1s2s3s2s1 : 2
Special Properties :
   Degenerate
   Universal
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {2,14,16,2} of size 1792
Vertex Figure Of :
   {2,2,14,16} of size 1792
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {2,14,8}*448
   4-fold quotients : {2,14,4}*224
   7-fold quotients : {2,2,16}*128
   8-fold quotients : {2,14,2}*112
   14-fold quotients : {2,2,8}*64
   16-fold quotients : {2,7,2}*56
   28-fold quotients : {2,2,4}*32
   56-fold quotients : {2,2,2}*16
Covers (Minimal Covers in Boldface) :
   2-fold covers : {2,28,16}*1792a, {4,14,16}*1792, {2,14,32}*1792
Permutation Representation (GAP) :
s0 := (1,2);;
s1 := (  4,  9)(  5,  8)(  6,  7)( 11, 16)( 12, 15)( 13, 14)( 18, 23)( 19, 22)
( 20, 21)( 25, 30)( 26, 29)( 27, 28)( 32, 37)( 33, 36)( 34, 35)( 39, 44)
( 40, 43)( 41, 42)( 46, 51)( 47, 50)( 48, 49)( 53, 58)( 54, 57)( 55, 56)
( 60, 65)( 61, 64)( 62, 63)( 67, 72)( 68, 71)( 69, 70)( 74, 79)( 75, 78)
( 76, 77)( 81, 86)( 82, 85)( 83, 84)( 88, 93)( 89, 92)( 90, 91)( 95,100)
( 96, 99)( 97, 98)(102,107)(103,106)(104,105)(109,114)(110,113)(111,112);;
s2 := (  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, 46)( 32, 45)( 33, 51)
( 34, 50)( 35, 49)( 36, 48)( 37, 47)( 38, 53)( 39, 52)( 40, 58)( 41, 57)
( 42, 56)( 43, 55)( 44, 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);;
s3 := (  3, 59)(  4, 60)(  5, 61)(  6, 62)(  7, 63)(  8, 64)(  9, 65)( 10, 66)
( 11, 67)( 12, 68)( 13, 69)( 14, 70)( 15, 71)( 16, 72)( 17, 80)( 18, 81)
( 19, 82)( 20, 83)( 21, 84)( 22, 85)( 23, 86)( 24, 73)( 25, 74)( 26, 75)
( 27, 76)( 28, 77)( 29, 78)( 30, 79)( 31,101)( 32,102)( 33,103)( 34,104)
( 35,105)( 36,106)( 37,107)( 38,108)( 39,109)( 40,110)( 41,111)( 42,112)
( 43,113)( 44,114)( 45, 87)( 46, 88)( 47, 89)( 48, 90)( 49, 91)( 50, 92)
( 51, 93)( 52, 94)( 53, 95)( 54, 96)( 55, 97)( 56, 98)( 57, 99)( 58,100);;
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, 
s1*s2*s3*s2*s1*s2*s3*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, 
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(114)!(1,2);
s1 := Sym(114)!(  4,  9)(  5,  8)(  6,  7)( 11, 16)( 12, 15)( 13, 14)( 18, 23)
( 19, 22)( 20, 21)( 25, 30)( 26, 29)( 27, 28)( 32, 37)( 33, 36)( 34, 35)
( 39, 44)( 40, 43)( 41, 42)( 46, 51)( 47, 50)( 48, 49)( 53, 58)( 54, 57)
( 55, 56)( 60, 65)( 61, 64)( 62, 63)( 67, 72)( 68, 71)( 69, 70)( 74, 79)
( 75, 78)( 76, 77)( 81, 86)( 82, 85)( 83, 84)( 88, 93)( 89, 92)( 90, 91)
( 95,100)( 96, 99)( 97, 98)(102,107)(103,106)(104,105)(109,114)(110,113)
(111,112);
s2 := Sym(114)!(  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, 46)( 32, 45)
( 33, 51)( 34, 50)( 35, 49)( 36, 48)( 37, 47)( 38, 53)( 39, 52)( 40, 58)
( 41, 57)( 42, 56)( 43, 55)( 44, 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);
s3 := Sym(114)!(  3, 59)(  4, 60)(  5, 61)(  6, 62)(  7, 63)(  8, 64)(  9, 65)
( 10, 66)( 11, 67)( 12, 68)( 13, 69)( 14, 70)( 15, 71)( 16, 72)( 17, 80)
( 18, 81)( 19, 82)( 20, 83)( 21, 84)( 22, 85)( 23, 86)( 24, 73)( 25, 74)
( 26, 75)( 27, 76)( 28, 77)( 29, 78)( 30, 79)( 31,101)( 32,102)( 33,103)
( 34,104)( 35,105)( 36,106)( 37,107)( 38,108)( 39,109)( 40,110)( 41,111)
( 42,112)( 43,113)( 44,114)( 45, 87)( 46, 88)( 47, 89)( 48, 90)( 49, 91)
( 50, 92)( 51, 93)( 52, 94)( 53, 95)( 54, 96)( 55, 97)( 56, 98)( 57, 99)
( 58,100);
poly := sub<Sym(114)|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, s1*s2*s3*s2*s1*s2*s3*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, 
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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