Part of the Atlas of Small Regular Polytopes

Polytope of Type {10,8,3}

Atlas Canonical Name {10,8,3}*1920

Overview

Group
SmallGroup(1920,238599)
Rank
4
Schläfli Type
{10,8,3}
Vertices, edges, …
10, 160, 48, 12
Order of s0s1s2s3
30
Order of s0s1s2s3s2s1
2
Also known as
{{10,8|2},{8,3}6}. if this polytope has another name.

Special Properties

  • Universal
  • Orientable
  • Flat

Quotients maximal quotients in bold

4-fold

5-fold

16-fold

20-fold

32-fold

40-fold

80-fold

Covers minimal covers in bold

None in this atlas.

Irregular Quotients of which this is a minimal cover

Click an entry to reveal its facets and vertex figures.

P/N, where N=<(s1*s2)^4> of order 2

8 facets

10 vertex figures

  • 10 of 2-fold non-regular quotient of {8,3}*192
P/N, where N=<(s1*s2)^2> of order 4

6 facets

10 vertex figures

  • 10 of 4-fold non-regular quotient of {8,3}*192
P/N, where N=<(s1*s2)^4, s1*s2*s3*(s2*s1)^3*s2*s3*s2> of order 4

4 facets

10 vertex figures

  • 10 of 4-fold non-regular quotient of {8,3}*192

Representations

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*s2*s1*s3*s2*s1*s3*s2*s1*s3*s2*s1*s3*s2*s1*s2*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*s2*s1*s3*s2*s1*s3*s2*s1*s3*s2*s1*s3*s2*s1*s2*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.