Polytope of Type {16,4,2,5}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {16,4,2,5}*1280a
if this polytope has a name.
Group : SmallGroup(1280,323301)
Rank : 5
Schlafli Type : {16,4,2,5}
Number of vertices, edges, etc : 16, 32, 4, 5, 5
Order of s₀s₁s₂s₃s₄ : 80
Order of s₀s₁s₂s₃s₄s₃s₂s₁ : 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) :
   2-fold quotients : {8,4,2,5}*640a, {16,2,2,5}*640
   4-fold quotients : {4,4,2,5}*320, {8,2,2,5}*320
   8-fold quotients : {2,4,2,5}*160, {4,2,2,5}*160
   16-fold quotients : {2,2,2,5}*80
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

s0 := ( 1,33)( 2,34)( 3,36)( 4,35)( 5,37)( 6,38)( 7,40)( 8,39)( 9,43)(10,44)
(11,41)(12,42)(13,47)(14,48)(15,45)(16,46)(17,49)(18,50)(19,52)(20,51)(21,53)
(22,54)(23,56)(24,55)(25,59)(26,60)(27,57)(28,58)(29,63)(30,64)(31,61)
(32,62);;
s1 := ( 3, 4)( 7, 8)( 9,11)(10,12)(13,15)(14,16)(17,21)(18,22)(19,24)(20,23)
(25,31)(26,32)(27,29)(28,30)(33,41)(34,42)(35,44)(36,43)(37,45)(38,46)(39,48)
(40,47)(49,61)(50,62)(51,64)(52,63)(53,57)(54,58)(55,60)(56,59);;
s2 := ( 1,17)( 2,18)( 3,19)( 4,20)( 5,21)( 6,22)( 7,23)( 8,24)( 9,25)(10,26)
(11,27)(12,28)(13,29)(14,30)(15,31)(16,32)(33,49)(34,50)(35,51)(36,52)(37,53)
(38,54)(39,55)(40,56)(41,57)(42,58)(43,59)(44,60)(45,61)(46,62)(47,63)
(48,64);;
s3 := (66,67)(68,69);;
s4 := (65,66)(67,68);;
poly := Group([s0,s1,s2,s3,s4]);;

Finitely Presented Group Representation (GAP) :

F := FreeGroup("s0","s1","s2","s3","s4");;
s0 := F.1;;  s1 := F.2;;  s2 := F.3;;  s3 := F.4;;  s4 := F.5;;  
rels := [ s0*s0, s1*s1, s2*s2, s3*s3, s4*s4, s0*s2*s0*s2, 
s0*s3*s0*s3, s1*s3*s1*s3, s2*s3*s2*s3, 
s0*s4*s0*s4, s1*s4*s1*s4, s2*s4*s2*s4, 
s0*s1*s2*s1*s0*s1*s2*s1, s1*s2*s1*s2*s1*s2*s1*s2, 
s3*s4*s3*s4*s3*s4*s3*s4*s3*s4, s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 ];;
poly := F / rels;;

Permutation Representation (Magma) :

s0 := Sym(69)!( 1,33)( 2,34)( 3,36)( 4,35)( 5,37)( 6,38)( 7,40)( 8,39)( 9,43)
(10,44)(11,41)(12,42)(13,47)(14,48)(15,45)(16,46)(17,49)(18,50)(19,52)(20,51)
(21,53)(22,54)(23,56)(24,55)(25,59)(26,60)(27,57)(28,58)(29,63)(30,64)(31,61)
(32,62);
s1 := Sym(69)!( 3, 4)( 7, 8)( 9,11)(10,12)(13,15)(14,16)(17,21)(18,22)(19,24)
(20,23)(25,31)(26,32)(27,29)(28,30)(33,41)(34,42)(35,44)(36,43)(37,45)(38,46)
(39,48)(40,47)(49,61)(50,62)(51,64)(52,63)(53,57)(54,58)(55,60)(56,59);
s2 := Sym(69)!( 1,17)( 2,18)( 3,19)( 4,20)( 5,21)( 6,22)( 7,23)( 8,24)( 9,25)
(10,26)(11,27)(12,28)(13,29)(14,30)(15,31)(16,32)(33,49)(34,50)(35,51)(36,52)
(37,53)(38,54)(39,55)(40,56)(41,57)(42,58)(43,59)(44,60)(45,61)(46,62)(47,63)
(48,64);
s3 := Sym(69)!(66,67)(68,69);
s4 := Sym(69)!(65,66)(67,68);
poly := sub<Sym(69)|s0,s1,s2,s3,s4>;

Finitely Presented Group Representation (Magma) :

poly<s0,s1,s2,s3,s4> := Group< s0,s1,s2,s3,s4 | s0*s0, s1*s1, s2*s2, 
s3*s3, s4*s4, s0*s2*s0*s2, s0*s3*s0*s3, 
s1*s3*s1*s3, s2*s3*s2*s3, s0*s4*s0*s4, 
s1*s4*s1*s4, s2*s4*s2*s4, s0*s1*s2*s1*s0*s1*s2*s1, 
s1*s2*s1*s2*s1*s2*s1*s2, s3*s4*s3*s4*s3*s4*s3*s4*s3*s4, 
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 >;

to this polytope