Polytope of Type {2,7,4}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,7,4}*1792
if this polytope has a name.
Group : SmallGroup(1792,1083553)
Rank : 4
Schlafli Type : {2,7,4}
Number of vertices, edges, etc : 2, 112, 224, 64
Order of s₀s₁s₂s₃ : 14
Order of s₀s₁s₂s₃s₂s₁ : 2
Special Properties :
   Degenerate
   Universal
   Non-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 := ( 4,51)( 5,19)( 6,35)( 7,27)( 8,43)( 9,11)(10,59)(12,57)(13,25)(14,41)
(15,33)(16,49)(18,65)(20,53)(22,37)(23,29)(24,45)(26,61)(28,55)(30,39)(32,47)
(34,63)(36,54)(40,46)(42,62)(44,56)(50,64)(58,60);;
s2 := ( 4,35)( 5,27)( 6,59)( 7,51)( 8,19)( 9,43)(10,11)(12,42)(13,34)(14,66)
(15,58)(16,26)(17,50)(20,40)(21,32)(22,64)(23,56)(25,48)(28,37)(30,61)(31,53)
(33,45)(38,60)(39,52)(41,44)(46,65)(47,57)(54,63);;
s3 := ( 3,21)( 4,22)( 5,19)( 6,20)( 7,25)( 8,26)( 9,23)(10,24)(11,29)(12,30)
(13,27)(14,28)(15,33)(16,34)(17,31)(18,32)(35,53)(36,54)(37,51)(38,52)(39,57)
(40,58)(41,55)(42,56)(43,61)(44,62)(45,59)(46,60)(47,65)(48,66)(49,63)
(50,64);;
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*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, 
s1*s2*s3*s2*s1*s2*s3*s2*s1*s2*s3*s2*s1*s2*s3*s2, 
s1*s2*s3*s1*s2*s3*s1*s2*s3*s1*s2*s3*s1*s2*s3*s1*s2*s3*s1*s2*s3 ];;
poly := F / rels;;

Permutation Representation (Magma) :

s0 := Sym(66)!(1,2);
s1 := Sym(66)!( 4,51)( 5,19)( 6,35)( 7,27)( 8,43)( 9,11)(10,59)(12,57)(13,25)
(14,41)(15,33)(16,49)(18,65)(20,53)(22,37)(23,29)(24,45)(26,61)(28,55)(30,39)
(32,47)(34,63)(36,54)(40,46)(42,62)(44,56)(50,64)(58,60);
s2 := Sym(66)!( 4,35)( 5,27)( 6,59)( 7,51)( 8,19)( 9,43)(10,11)(12,42)(13,34)
(14,66)(15,58)(16,26)(17,50)(20,40)(21,32)(22,64)(23,56)(25,48)(28,37)(30,61)
(31,53)(33,45)(38,60)(39,52)(41,44)(46,65)(47,57)(54,63);
s3 := Sym(66)!( 3,21)( 4,22)( 5,19)( 6,20)( 7,25)( 8,26)( 9,23)(10,24)(11,29)
(12,30)(13,27)(14,28)(15,33)(16,34)(17,31)(18,32)(35,53)(36,54)(37,51)(38,52)
(39,57)(40,58)(41,55)(42,56)(43,61)(44,62)(45,59)(46,60)(47,65)(48,66)(49,63)
(50,64);
poly := sub<Sym(66)|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*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, 
s1*s2*s3*s2*s1*s2*s3*s2*s1*s2*s3*s2*s1*s2*s3*s2, 
s1*s2*s3*s1*s2*s3*s1*s2*s3*s1*s2*s3*s1*s2*s3*s1*s2*s3*s1*s2*s3 >;

to this polytope