Polytope of Type {2,56,4}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,56,4}*1792b
if this polytope has a name.
Group : SmallGroup(1792,323570)
Rank : 4
Schlafli Type : {2,56,4}
Number of vertices, edges, etc : 2, 112, 224, 8
Order of s₀s₁s₂s₃ : 28
Order of s₀s₁s₂s₃s₂s₁ : 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 : {2,28,4}*896
   4-fold quotients : {2,28,4}*448
   7-fold quotients : {2,8,4}*256b
   8-fold quotients : {2,28,2}*224, {2,14,4}*224
   14-fold quotients : {2,4,4}*128
   16-fold quotients : {2,14,2}*112
   28-fold quotients : {2,4,4}*64
   32-fold quotients : {2,7,2}*56
   56-fold quotients : {2,2,4}*32, {2,4,2}*32
   112-fold quotients : {2,2,2}*16
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

s0 := (1,2);;
s1 := (  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, 73)( 18, 79)
( 19, 78)( 20, 77)( 21, 76)( 22, 75)( 23, 74)( 24, 80)( 25, 86)( 26, 85)
( 27, 84)( 28, 83)( 29, 82)( 30, 81)( 31,108)( 32,114)( 33,113)( 34,112)
( 35,111)( 36,110)( 37,109)( 38,101)( 39,107)( 40,106)( 41,105)( 42,104)
( 43,103)( 44,102)( 45, 94)( 46,100)( 47, 99)( 48, 98)( 49, 97)( 50, 96)
( 51, 95)( 52, 87)( 53, 93)( 54, 92)( 55, 91)( 56, 90)( 57, 89)( 58, 88);;
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, 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);;
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, 73)( 18, 74)
( 19, 75)( 20, 76)( 21, 77)( 22, 78)( 23, 79)( 24, 80)( 25, 81)( 26, 82)
( 27, 83)( 28, 84)( 29, 85)( 30, 86)( 31, 87)( 32, 88)( 33, 89)( 34, 90)
( 35, 91)( 36, 92)( 37, 93)( 38, 94)( 39, 95)( 40, 96)( 41, 97)( 42, 98)
( 43, 99)( 44,100)( 45,101)( 46,102)( 47,103)( 48,104)( 49,105)( 50,106)
( 51,107)( 52,108)( 53,109)( 54,110)( 55,111)( 56,112)( 57,113)( 58,114);;
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, 
s2*s3*s2*s3*s2*s3*s2*s3, s1*s2*s3*s2*s1*s2*s1*s2*s1*s2*s3*s2*s1*s2*s1*s2, 
s1*s2*s3*s2*s1*s2*s3*s2*s1*s2*s3*s2*s1*s2*s3*s2, 
s2*s1*s2*s1*s2*s1*s2*s3*s1*s2*s3*s1*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*s3*s1*s2*s1 ];;
poly := F / rels;;

Permutation Representation (Magma) :

s0 := Sym(114)!(1,2);
s1 := Sym(114)!(  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, 73)
( 18, 79)( 19, 78)( 20, 77)( 21, 76)( 22, 75)( 23, 74)( 24, 80)( 25, 86)
( 26, 85)( 27, 84)( 28, 83)( 29, 82)( 30, 81)( 31,108)( 32,114)( 33,113)
( 34,112)( 35,111)( 36,110)( 37,109)( 38,101)( 39,107)( 40,106)( 41,105)
( 42,104)( 43,103)( 44,102)( 45, 94)( 46,100)( 47, 99)( 48, 98)( 49, 97)
( 50, 96)( 51, 95)( 52, 87)( 53, 93)( 54, 92)( 55, 91)( 56, 90)( 57, 89)
( 58, 88);
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, 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);
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, 73)
( 18, 74)( 19, 75)( 20, 76)( 21, 77)( 22, 78)( 23, 79)( 24, 80)( 25, 81)
( 26, 82)( 27, 83)( 28, 84)( 29, 85)( 30, 86)( 31, 87)( 32, 88)( 33, 89)
( 34, 90)( 35, 91)( 36, 92)( 37, 93)( 38, 94)( 39, 95)( 40, 96)( 41, 97)
( 42, 98)( 43, 99)( 44,100)( 45,101)( 46,102)( 47,103)( 48,104)( 49,105)
( 50,106)( 51,107)( 52,108)( 53,109)( 54,110)( 55,111)( 56,112)( 57,113)
( 58,114);
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, s2*s3*s2*s3*s2*s3*s2*s3, 
s1*s2*s3*s2*s1*s2*s1*s2*s1*s2*s3*s2*s1*s2*s1*s2, 
s1*s2*s3*s2*s1*s2*s3*s2*s1*s2*s3*s2*s1*s2*s3*s2, 
s2*s1*s2*s1*s2*s1*s2*s3*s1*s2*s3*s1*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*s3*s1*s2*s1 >;

to this polytope