Polytope of Type {10,8,3}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {10,8,3}*1920
Also Known As : {{10,8|2},{8,3}₆}. if this polytope has another name.
Group : SmallGroup(1920,238599)
Rank : 4
Schlafli Type : {10,8,3}
Number of vertices, edges, etc : 10, 160, 48, 12
Order of s₀s₁s₂s₃ : 30
Order of s₀s₁s₂s₃s₂s₁ : 2
Special Properties :
   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) :
   4-fold quotients : {10,4,3}*480
   5-fold quotients : {2,8,3}*384
   16-fold quotients : {10,2,3}*120
   20-fold quotients : {2,4,3}*96
   32-fold quotients : {5,2,3}*60
   40-fold quotients : {2,4,3}*48
   80-fold quotients : {2,2,3}*24
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

s0 := (17,65)(18,66)(19,67)(20,68)(21,69)(22,70)(23,71)(24,72)(25,73)(26,74)
(27,75)(28,76)(29,77)(30,78)(31,79)(32,80)(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);;
s1 := ( 1,25)( 2,26)( 3,27)( 4,28)( 5,30)( 6,29)( 7,32)( 8,31)( 9,17)(10,18)
(11,19)(12,20)(13,22)(14,21)(15,24)(16,23)(33,73)(34,74)(35,75)(36,76)(37,78)
(38,77)(39,80)(40,79)(41,65)(42,66)(43,67)(44,68)(45,70)(46,69)(47,72)(48,71)
(49,57)(50,58)(51,59)(52,60)(53,62)(54,61)(55,64)(56,63);;
s2 := ( 3, 4)( 5, 6)( 9,13)(10,14)(11,16)(12,15)(19,20)(21,22)(25,29)(26,30)
(27,32)(28,31)(35,36)(37,38)(41,45)(42,46)(43,48)(44,47)(51,52)(53,54)(57,61)
(58,62)(59,64)(60,63)(67,68)(69,70)(73,77)(74,78)(75,80)(76,79);;
s3 := ( 2, 4)( 5,14)( 6,15)( 7,16)( 8,13)(10,12)(18,20)(21,30)(22,31)(23,32)
(24,29)(26,28)(34,36)(37,46)(38,47)(39,48)(40,45)(42,44)(50,52)(53,62)(54,63)
(55,64)(56,61)(58,60)(66,68)(69,78)(70,79)(71,80)(72,77)(74,76);;
poly := Group([s0,s1,s2,s3]);;

Finitely Presented Group Representation (GAP) :

F := FreeGroup("s0","s1","s2","s3");;
s0 := F.1;;  s1 := F.2;;  s2 := F.3;;  s3 := F.4;;  
rels := [ s0*s0, s1*s1, s2*s2, s3*s3, s0*s2*s0*s2, 
s0*s3*s0*s3, s1*s3*s1*s3, s2*s3*s2*s3*s2*s3, 
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*s3*s2*s1*s3*s2*s1*s3*s2*s1*s3*s2*s1*s3*s2*s1*s3*s2, 
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)!(17,65)(18,66)(19,67)(20,68)(21,69)(22,70)(23,71)(24,72)(25,73)
(26,74)(27,75)(28,76)(29,77)(30,78)(31,79)(32,80)(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);
s1 := Sym(80)!( 1,25)( 2,26)( 3,27)( 4,28)( 5,30)( 6,29)( 7,32)( 8,31)( 9,17)
(10,18)(11,19)(12,20)(13,22)(14,21)(15,24)(16,23)(33,73)(34,74)(35,75)(36,76)
(37,78)(38,77)(39,80)(40,79)(41,65)(42,66)(43,67)(44,68)(45,70)(46,69)(47,72)
(48,71)(49,57)(50,58)(51,59)(52,60)(53,62)(54,61)(55,64)(56,63);
s2 := Sym(80)!( 3, 4)( 5, 6)( 9,13)(10,14)(11,16)(12,15)(19,20)(21,22)(25,29)
(26,30)(27,32)(28,31)(35,36)(37,38)(41,45)(42,46)(43,48)(44,47)(51,52)(53,54)
(57,61)(58,62)(59,64)(60,63)(67,68)(69,70)(73,77)(74,78)(75,80)(76,79);
s3 := Sym(80)!( 2, 4)( 5,14)( 6,15)( 7,16)( 8,13)(10,12)(18,20)(21,30)(22,31)
(23,32)(24,29)(26,28)(34,36)(37,46)(38,47)(39,48)(40,45)(42,44)(50,52)(53,62)
(54,63)(55,64)(56,61)(58,60)(66,68)(69,78)(70,79)(71,80)(72,77)(74,76);
poly := sub<Sym(80)|s0,s1,s2,s3>;

Finitely Presented Group Representation (Magma) :

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

References : None.
to this polytope