Polytope of Type {7,4}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {7,4}*896
if this polytope has a name.
Group : SmallGroup(896,19344)
Rank : 3
Schlafli Type : {7,4}
Number of vertices, edges, etc : 112, 224, 64
Order of s₀s₁s₂ : 7
Order of s₀s₁s₂s₁ : 4
Special Properties :
   Compact Hyperbolic Quotient
   Locally Spherical
   Non-Orientable
   Self-Petrie
Related Polytopes :
   Facet
   Vertex Figure
   Dual
   Petrial
   Skewing Operation
Facet Of :
   {7,4,2} of size 1792
Vertex Figure Of :
   {2,7,4} of size 1792
Quotients (Maximal Quotients in Boldface) :
   No Regular Quotients.
Covers (Minimal Covers in Boldface) :
   2-fold covers : {7,4}*1792a, {7,4}*1792b, {7,8}*1792a, {7,8}*1792b, {7,8}*1792c, {7,8}*1792d, {14,4}*1792a, {14,4}*1792b, {7,4}*1792c, {14,4}*1792c, {14,4}*1792d
Permutation Representation (GAP) :

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

Finitely Presented Group Representation (GAP) :

F := FreeGroup("s0","s1","s2");;
s0 := F.1;;  s1 := F.2;;  s2 := F.3;;  
rels := [ s0*s0, s1*s1, s2*s2, s0*s2*s0*s2, s1*s2*s1*s2*s1*s2*s1*s2, 
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1, 
s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1, 
s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1*s2 ];;
poly := F / rels;;

Permutation Representation (Magma) :

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

Finitely Presented Group Representation (Magma) :

poly<s0,s1,s2> := Group< s0,s1,s2 | s0*s0, s1*s1, s2*s2, 
s0*s2*s0*s2, s1*s2*s1*s2*s1*s2*s1*s2, 
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1, 
s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1, 
s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1*s2 >;

References : None.
to this polytope