Polytope of Type {4,7}

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

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