Polytope of Type {2,28,8}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,28,8}*896a
if this polytope has a name.
Group : SmallGroup(896,10954)
Rank : 4
Schlafli Type : {2,28,8}
Number of vertices, edges, etc : 2, 28, 112, 8
Order of s₀s₁s₂s₃ : 56
Order of s₀s₁s₂s₃s₂s₁ : 2
Special Properties :
   Degenerate
   Universal
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {2,28,8,2} of size 1792
Vertex Figure Of :
   {2,2,28,8} of size 1792
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {2,28,4}*448, {2,14,8}*448
   4-fold quotients : {2,28,2}*224, {2,14,4}*224
   7-fold quotients : {2,4,8}*128a
   8-fold quotients : {2,14,2}*112
   14-fold quotients : {2,4,4}*64, {2,2,8}*64
   16-fold quotients : {2,7,2}*56
   28-fold quotients : {2,2,4}*32, {2,4,2}*32
   56-fold quotients : {2,2,2}*16
Covers (Minimal Covers in Boldface) :
   2-fold covers : {2,28,8}*1792a, {2,56,8}*1792a, {2,56,8}*1792c, {4,28,8}*1792a, {2,28,16}*1792a, {2,28,16}*1792b
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)
( 59, 87)( 60, 93)( 61, 92)( 62, 91)( 63, 90)( 64, 89)( 65, 88)( 66, 94)
( 67,100)( 68, 99)( 69, 98)( 70, 97)( 71, 96)( 72, 95)( 73,101)( 74,107)
( 75,106)( 76,105)( 77,104)( 78,103)( 79,102)( 80,108)( 81,114)( 82,113)
( 83,112)( 84,111)( 85,110)( 86,109);;
s2 := (  3, 60)(  4, 59)(  5, 65)(  6, 64)(  7, 63)(  8, 62)(  9, 61)( 10, 67)
( 11, 66)( 12, 72)( 13, 71)( 14, 70)( 15, 69)( 16, 68)( 17, 81)( 18, 80)
( 19, 86)( 20, 85)( 21, 84)( 22, 83)( 23, 82)( 24, 74)( 25, 73)( 26, 79)
( 27, 78)( 28, 77)( 29, 76)( 30, 75)( 31, 88)( 32, 87)( 33, 93)( 34, 92)
( 35, 91)( 36, 90)( 37, 89)( 38, 95)( 39, 94)( 40,100)( 41, 99)( 42, 98)
( 43, 97)( 44, 96)( 45,109)( 46,108)( 47,114)( 48,113)( 49,112)( 50,111)
( 51,110)( 52,102)( 53,101)( 54,107)( 55,106)( 56,105)( 57,104)( 58,103);;
s3 := ( 17, 24)( 18, 25)( 19, 26)( 20, 27)( 21, 28)( 22, 29)( 23, 30)( 45, 52)
( 46, 53)( 47, 54)( 48, 55)( 49, 56)( 50, 57)( 51, 58)( 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)( 87,101)( 88,102)( 89,103)( 90,104)
( 91,105)( 92,106)( 93,107)( 94,108)( 95,109)( 96,110)( 97,111)( 98,112)
( 99,113)(100,114);;
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, 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*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(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)( 59, 87)( 60, 93)( 61, 92)( 62, 91)( 63, 90)( 64, 89)( 65, 88)
( 66, 94)( 67,100)( 68, 99)( 69, 98)( 70, 97)( 71, 96)( 72, 95)( 73,101)
( 74,107)( 75,106)( 76,105)( 77,104)( 78,103)( 79,102)( 80,108)( 81,114)
( 82,113)( 83,112)( 84,111)( 85,110)( 86,109);
s2 := Sym(114)!(  3, 60)(  4, 59)(  5, 65)(  6, 64)(  7, 63)(  8, 62)(  9, 61)
( 10, 67)( 11, 66)( 12, 72)( 13, 71)( 14, 70)( 15, 69)( 16, 68)( 17, 81)
( 18, 80)( 19, 86)( 20, 85)( 21, 84)( 22, 83)( 23, 82)( 24, 74)( 25, 73)
( 26, 79)( 27, 78)( 28, 77)( 29, 76)( 30, 75)( 31, 88)( 32, 87)( 33, 93)
( 34, 92)( 35, 91)( 36, 90)( 37, 89)( 38, 95)( 39, 94)( 40,100)( 41, 99)
( 42, 98)( 43, 97)( 44, 96)( 45,109)( 46,108)( 47,114)( 48,113)( 49,112)
( 50,111)( 51,110)( 52,102)( 53,101)( 54,107)( 55,106)( 56,105)( 57,104)
( 58,103);
s3 := Sym(114)!( 17, 24)( 18, 25)( 19, 26)( 20, 27)( 21, 28)( 22, 29)( 23, 30)
( 45, 52)( 46, 53)( 47, 54)( 48, 55)( 49, 56)( 50, 57)( 51, 58)( 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)( 87,101)( 88,102)( 89,103)
( 90,104)( 91,105)( 92,106)( 93,107)( 94,108)( 95,109)( 96,110)( 97,111)
( 98,112)( 99,113)(100,114);
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, 
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*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 >;

to this polytope