Part of the Atlas of Small Regular Polytopes

Polytope of Type {10,6,3}

Atlas Canonical Name {10,6,3}*1920

Overview

Group
SmallGroup(1920,238599)
Rank
4
Schläfli Type
{10,6,3}
Vertices, edges, …
10, 160, 48, 16
Order of s0s1s2s3
40
Order of s0s1s2s3s2s1
2
Also known as
{{10,6|2},{6,3}8}. if this polytope has another name.

Special Properties

  • Universal
  • Orientable
  • Flat

Quotients maximal quotients in bold

4-fold

5-fold

20-fold

40-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=<((s2*s1)^2*s2*s3)^2> of order 2

8 facets

10 vertex figures

  • 10 of 2-fold non-regular quotient of {6,3}*192
P/N, where N=<s1*s2*s1*s3*(s2*s1)^2*s2*s3*s2> of order 4

4 facets

10 vertex figures

  • 10 of 4-fold non-regular quotient of {6,3}*192
P/N, where N=<s1*s2*s1*s3*(s2*s1)^2*s3*s2> of order 4

4 facets

10 vertex figures

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

References

None.

to this polytope.