Polytope of Type {2,4,4}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,4,4}*1936
if this polytope has a name.
Group : SmallGroup(1936,161)
Rank : 4
Schlafli Type : {2,4,4}
Number of vertices, edges, etc : 2, 121, 242, 121
Order of s₀s₁s₂s₃ : 22
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) :
   No Regular Quotients.
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

s0 := (1,2);;
s1 := ( 14,113)( 15,114)( 16,115)( 17,116)( 18,117)( 19,118)( 20,119)( 21,120)
( 22,121)( 23,122)( 24,123)( 25,102)( 26,103)( 27,104)( 28,105)( 29,106)
( 30,107)( 31,108)( 32,109)( 33,110)( 34,111)( 35,112)( 36, 91)( 37, 92)
( 38, 93)( 39, 94)( 40, 95)( 41, 96)( 42, 97)( 43, 98)( 44, 99)( 45,100)
( 46,101)( 47, 80)( 48, 81)( 49, 82)( 50, 83)( 51, 84)( 52, 85)( 53, 86)
( 54, 87)( 55, 88)( 56, 89)( 57, 90)( 58, 69)( 59, 70)( 60, 71)( 61, 72)
( 62, 73)( 63, 74)( 64, 75)( 65, 76)( 66, 77)( 67, 78)( 68, 79);;
s2 := (  4, 14)(  5, 25)(  6, 36)(  7, 47)(  8, 58)(  9, 69)( 10, 80)( 11, 91)
( 12,102)( 13,113)( 16, 26)( 17, 37)( 18, 48)( 19, 59)( 20, 70)( 21, 81)
( 22, 92)( 23,103)( 24,114)( 28, 38)( 29, 49)( 30, 60)( 31, 71)( 32, 82)
( 33, 93)( 34,104)( 35,115)( 40, 50)( 41, 61)( 42, 72)( 43, 83)( 44, 94)
( 45,105)( 46,116)( 52, 62)( 53, 73)( 54, 84)( 55, 95)( 56,106)( 57,117)
( 64, 74)( 65, 85)( 66, 96)( 67,107)( 68,118)( 76, 86)( 77, 97)( 78,108)
( 79,119)( 88, 98)( 89,109)( 90,120)(100,110)(101,121)(112,122);;
s3 := (  3,  4)(  5, 13)(  6, 12)(  7, 11)(  8, 10)( 14, 15)( 16, 24)( 17, 23)
( 18, 22)( 19, 21)( 25, 26)( 27, 35)( 28, 34)( 29, 33)( 30, 32)( 36, 37)
( 38, 46)( 39, 45)( 40, 44)( 41, 43)( 47, 48)( 49, 57)( 50, 56)( 51, 55)
( 52, 54)( 58, 59)( 60, 68)( 61, 67)( 62, 66)( 63, 65)( 69, 70)( 71, 79)
( 72, 78)( 73, 77)( 74, 76)( 80, 81)( 82, 90)( 83, 89)( 84, 88)( 85, 87)
( 91, 92)( 93,101)( 94,100)( 95, 99)( 96, 98)(102,103)(104,112)(105,111)
(106,110)(107,109)(113,114)(115,123)(116,122)(117,121)(118,120);;
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*s1*s2*s1*s2*s1*s2, s2*s3*s2*s3*s2*s3*s2*s3, 
s1*s2*s3*s2*s1*s2*s3*s2*s1*s2*s3*s2*s1*s2*s3*s2*s1*s2*s3*s2*s1*s2*s3*s2*s1*s2*s3*s2*s1*s2*s3*s2*s1*s2*s3*s2*s1*s2*s3*s2*s1*s2*s3*s2 ];;
poly := F / rels;;

Permutation Representation (Magma) :

s0 := Sym(123)!(1,2);
s1 := Sym(123)!( 14,113)( 15,114)( 16,115)( 17,116)( 18,117)( 19,118)( 20,119)
( 21,120)( 22,121)( 23,122)( 24,123)( 25,102)( 26,103)( 27,104)( 28,105)
( 29,106)( 30,107)( 31,108)( 32,109)( 33,110)( 34,111)( 35,112)( 36, 91)
( 37, 92)( 38, 93)( 39, 94)( 40, 95)( 41, 96)( 42, 97)( 43, 98)( 44, 99)
( 45,100)( 46,101)( 47, 80)( 48, 81)( 49, 82)( 50, 83)( 51, 84)( 52, 85)
( 53, 86)( 54, 87)( 55, 88)( 56, 89)( 57, 90)( 58, 69)( 59, 70)( 60, 71)
( 61, 72)( 62, 73)( 63, 74)( 64, 75)( 65, 76)( 66, 77)( 67, 78)( 68, 79);
s2 := Sym(123)!(  4, 14)(  5, 25)(  6, 36)(  7, 47)(  8, 58)(  9, 69)( 10, 80)
( 11, 91)( 12,102)( 13,113)( 16, 26)( 17, 37)( 18, 48)( 19, 59)( 20, 70)
( 21, 81)( 22, 92)( 23,103)( 24,114)( 28, 38)( 29, 49)( 30, 60)( 31, 71)
( 32, 82)( 33, 93)( 34,104)( 35,115)( 40, 50)( 41, 61)( 42, 72)( 43, 83)
( 44, 94)( 45,105)( 46,116)( 52, 62)( 53, 73)( 54, 84)( 55, 95)( 56,106)
( 57,117)( 64, 74)( 65, 85)( 66, 96)( 67,107)( 68,118)( 76, 86)( 77, 97)
( 78,108)( 79,119)( 88, 98)( 89,109)( 90,120)(100,110)(101,121)(112,122);
s3 := Sym(123)!(  3,  4)(  5, 13)(  6, 12)(  7, 11)(  8, 10)( 14, 15)( 16, 24)
( 17, 23)( 18, 22)( 19, 21)( 25, 26)( 27, 35)( 28, 34)( 29, 33)( 30, 32)
( 36, 37)( 38, 46)( 39, 45)( 40, 44)( 41, 43)( 47, 48)( 49, 57)( 50, 56)
( 51, 55)( 52, 54)( 58, 59)( 60, 68)( 61, 67)( 62, 66)( 63, 65)( 69, 70)
( 71, 79)( 72, 78)( 73, 77)( 74, 76)( 80, 81)( 82, 90)( 83, 89)( 84, 88)
( 85, 87)( 91, 92)( 93,101)( 94,100)( 95, 99)( 96, 98)(102,103)(104,112)
(105,111)(106,110)(107,109)(113,114)(115,123)(116,122)(117,121)(118,120);
poly := sub<Sym(123)|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*s1*s2*s1*s2*s1*s2, 
s2*s3*s2*s3*s2*s3*s2*s3, s1*s2*s3*s2*s1*s2*s3*s2*s1*s2*s3*s2*s1*s2*s3*s2*s1*s2*s3*s2*s1*s2*s3*s2*s1*s2*s3*s2*s1*s2*s3*s2*s1*s2*s3*s2*s1*s2*s3*s2*s1*s2*s3*s2 >;

to this polytope