Polytope of Type {2,56,4}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,56,4}*896a
if this polytope has a name.
Group : SmallGroup(896,10817)
Rank : 4
Schlafli Type : {2,56,4}
Number of vertices, edges, etc : 2, 56, 112, 4
Order of s₀s₁s₂s₃ : 56
Order of s₀s₁s₂s₃s₂s₁ : 2
Special Properties :
   Degenerate
   Universal
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {2,56,4,2} of size 1792
Vertex Figure Of :
   {2,2,56,4} of size 1792
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {2,28,4}*448, {2,56,2}*448
   4-fold quotients : {2,28,2}*224, {2,14,4}*224
   7-fold quotients : {2,8,4}*128a
   8-fold quotients : {2,14,2}*112
   14-fold quotients : {2,4,4}*64, {2,8,2}*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 : {2,56,4}*1792a, {2,56,8}*1792b, {2,56,8}*1792c, {4,56,4}*1792d, {2,112,4}*1792a, {2,112,4}*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)( 31, 38)( 32, 44)( 33, 43)( 34, 42)
( 35, 41)( 36, 40)( 37, 39)( 45, 52)( 46, 58)( 47, 57)( 48, 56)( 49, 55)
( 50, 54)( 51, 53)( 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, 74)( 18, 73)
( 19, 79)( 20, 78)( 21, 77)( 22, 76)( 23, 75)( 24, 81)( 25, 80)( 26, 86)
( 27, 85)( 28, 84)( 29, 83)( 30, 82)( 31, 95)( 32, 94)( 33,100)( 34, 99)
( 35, 98)( 36, 97)( 37, 96)( 38, 88)( 39, 87)( 40, 93)( 41, 92)( 42, 91)
( 43, 90)( 44, 89)( 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 := ( 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, 
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*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)( 31, 38)( 32, 44)( 33, 43)
( 34, 42)( 35, 41)( 36, 40)( 37, 39)( 45, 52)( 46, 58)( 47, 57)( 48, 56)
( 49, 55)( 50, 54)( 51, 53)( 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, 74)
( 18, 73)( 19, 79)( 20, 78)( 21, 77)( 22, 76)( 23, 75)( 24, 81)( 25, 80)
( 26, 86)( 27, 85)( 28, 84)( 29, 83)( 30, 82)( 31, 95)( 32, 94)( 33,100)
( 34, 99)( 35, 98)( 36, 97)( 37, 96)( 38, 88)( 39, 87)( 40, 93)( 41, 92)
( 42, 91)( 43, 90)( 44, 89)( 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)!( 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, 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*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