Polytope of Type {16,10}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {16,10}*320
Also Known As : {16,10|2}. if this polytope has another name.
Group : SmallGroup(320,537)
Rank : 3
Schlafli Type : {16,10}
Number of vertices, edges, etc : 16, 80, 10
Order of s₀s₁s₂ : 80
Order of s₀s₁s₂s₁ : 2
Special Properties :
   Compact Hyperbolic Quotient
   Locally Spherical
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {16,10,2} of size 640
   {16,10,4} of size 1280
   {16,10,5} of size 1600
   {16,10,6} of size 1920
   {16,10,3} of size 1920
   {16,10,5} of size 1920
Vertex Figure Of :
   {2,16,10} of size 640
   {4,16,10} of size 1280
   {4,16,10} of size 1280
   {6,16,10} of size 1920
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {8,10}*160
   4-fold quotients : {4,10}*80
   5-fold quotients : {16,2}*64
   8-fold quotients : {2,10}*40
   10-fold quotients : {8,2}*32
   16-fold quotients : {2,5}*20
   20-fold quotients : {4,2}*16
   40-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
   2-fold covers : {16,20}*640a, {32,10}*640
   3-fold covers : {48,10}*960, {16,30}*960
   4-fold covers : {16,20}*1280a, {16,40}*1280c, {16,40}*1280d, {32,20}*1280a, {32,20}*1280b, {64,10}*1280
   5-fold covers : {16,50}*1600, {80,10}*1600a, {80,10}*1600c
   6-fold covers : {16,60}*1920a, {48,20}*1920a, {32,30}*1920, {96,10}*1920
Permutation Representation (GAP) :

s0 := (11,16)(12,17)(13,18)(14,19)(15,20)(21,31)(22,32)(23,33)(24,34)(25,35)
(26,36)(27,37)(28,38)(29,39)(30,40)(41,61)(42,62)(43,63)(44,64)(45,65)(46,66)
(47,67)(48,68)(49,69)(50,70)(51,76)(52,77)(53,78)(54,79)(55,80)(56,71)(57,72)
(58,73)(59,74)(60,75);;
s1 := ( 1,41)( 2,45)( 3,44)( 4,43)( 5,42)( 6,46)( 7,50)( 8,49)( 9,48)(10,47)
(11,56)(12,60)(13,59)(14,58)(15,57)(16,51)(17,55)(18,54)(19,53)(20,52)(21,71)
(22,75)(23,74)(24,73)(25,72)(26,76)(27,80)(28,79)(29,78)(30,77)(31,61)(32,65)
(33,64)(34,63)(35,62)(36,66)(37,70)(38,69)(39,68)(40,67);;
s2 := ( 1, 2)( 3, 5)( 6, 7)( 8,10)(11,12)(13,15)(16,17)(18,20)(21,22)(23,25)
(26,27)(28,30)(31,32)(33,35)(36,37)(38,40)(41,42)(43,45)(46,47)(48,50)(51,52)
(53,55)(56,57)(58,60)(61,62)(63,65)(66,67)(68,70)(71,72)(73,75)(76,77)
(78,80);;
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*s2*s1*s0*s1*s2*s1, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*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*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 ];;
poly := F / rels;;

Permutation Representation (Magma) :

s0 := Sym(80)!(11,16)(12,17)(13,18)(14,19)(15,20)(21,31)(22,32)(23,33)(24,34)
(25,35)(26,36)(27,37)(28,38)(29,39)(30,40)(41,61)(42,62)(43,63)(44,64)(45,65)
(46,66)(47,67)(48,68)(49,69)(50,70)(51,76)(52,77)(53,78)(54,79)(55,80)(56,71)
(57,72)(58,73)(59,74)(60,75);
s1 := Sym(80)!( 1,41)( 2,45)( 3,44)( 4,43)( 5,42)( 6,46)( 7,50)( 8,49)( 9,48)
(10,47)(11,56)(12,60)(13,59)(14,58)(15,57)(16,51)(17,55)(18,54)(19,53)(20,52)
(21,71)(22,75)(23,74)(24,73)(25,72)(26,76)(27,80)(28,79)(29,78)(30,77)(31,61)
(32,65)(33,64)(34,63)(35,62)(36,66)(37,70)(38,69)(39,68)(40,67);
s2 := Sym(80)!( 1, 2)( 3, 5)( 6, 7)( 8,10)(11,12)(13,15)(16,17)(18,20)(21,22)
(23,25)(26,27)(28,30)(31,32)(33,35)(36,37)(38,40)(41,42)(43,45)(46,47)(48,50)
(51,52)(53,55)(56,57)(58,60)(61,62)(63,65)(66,67)(68,70)(71,72)(73,75)(76,77)
(78,80);
poly := sub<Sym(80)|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*s2*s1*s0*s1*s2*s1, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*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*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 >;

References : None.
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