Part of the Atlas of Small Regular Polytopes

Polytope of Type {3,8,10}

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

Overview

Group
SmallGroup(1920,238599)
Rank
4
Schläfli Type
{3,8,10}
Vertices, edges, …
12, 48, 160, 10
Order of s0s1s2s3
30
Order of s0s1s2s3s2s1
2
Also known as
{{3,8}6,{8,10|2}}. 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=<s0*s1*s0*(s2*s1)^3*s0*s2*s1> of order 2

10 facets

  • 10 of 2-fold non-regular quotient of {3,8}*192

8 vertex figures

P/N, where N=<s0*(s1*s0*s2)^2*s1> of order 4

10 facets

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

6 vertex figures

P/N, where N=<s0*s1*s2*s1*s0*(s2*s1)^2*s2> of order 4

10 facets

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

4 vertex figures

Representations

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

References

None.

to this polytope.