Polytope of Type {4,4} with group SmallGroup(392,37) - Atlas of Small Regular Polytopes

Overview

Group: SmallGroup(392,37)
Rank: 3
Schläfli Type: {4,4}
Vertices, edges, …: 49, 98, 49
Order of s₀s₁s₂: 14
Order of s₀s₁s₂s₁: 7
Also known as: {4,4}_(7,0), {4,4|7}. if this polytope has another name.

Special Properties

Toroidal
Locally Spherical
Orientable
Self-Dual

Quotients maximal quotients in bold

No regular quotients.

Covers minimal covers in bold

2-fold

{4,4}*784

4-fold

{4,4}*1568

Irregular Quotients of which this is a minimal cover

Click an entry to reveal its facets and vertex figures.

P/N, where N=<(s0*s1)^2*s2*s1*s0*s2*s1*s2> of order 7

7 facets

7 of {4}*8

7 vertex figures

7 of {4}*8

Representations

Permutation Representation (GAP)

s0 := ( 8,43)( 9,44)(10,45)(11,46)(12,47)(13,48)(14,49)(15,36)(16,37)(17,38)(18,39)(19,40)(20,41)(21,42)(22,29)(23,30)(24,31)(25,32)(26,33)(27,34)(28,35);;
s1 := ( 2, 8)( 3,15)( 4,22)( 5,29)( 6,36)( 7,43)(10,16)(11,23)(12,30)(13,37)(14,44)(18,24)(19,31)(20,38)(21,45)(26,32)(27,39)(28,46)(34,40)(35,47)(42,48);;
s2 := ( 1, 2)( 3, 7)( 4, 6)( 8, 9)(10,14)(11,13)(15,16)(17,21)(18,20)(22,23)(24,28)(25,27)(29,30)(31,35)(32,34)(36,37)(38,42)(39,41)(43,44)(45,49)(46,48);;
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, s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1 ];;
poly := F / rels;;

Permutation Representation (Magma)

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

References

None.

to this polytope.