Part of the Atlas of Small Regular Polytopes

Polytope of Type {10,4,4,3}

Atlas Canonical Name {10,4,4,3}*1920a

Overview

Group
SmallGroup(1920,238598)
Rank
5
Schläfli Type
{10,4,4,3}
Vertices, edges, …
10, 40, 16, 12, 3
Order of s0s1s2s3s4
30
Order of s0s1s2s3s4s3s2s1
2
Also known as
{{10,4|2},{4,4}4,{4,3}3}. if this polytope has another name.

Special Properties

  • Universal
  • Non-Orientable
  • Flat

Quotients maximal quotients in bold

4-fold

5-fold

8-fold

20-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*s3*s2)^2> of order 2

3 facets

10 vertex figures

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)( 3,19)( 4,20)( 5,22)( 6,21)( 7,24)( 8,23)( 9,27)(10,28)(11,25)(12,26)(13,32)(14,31)(15,30)(16,29)(33,65)(34,66)(35,67)(36,68)(37,70)(38,69)(39,72)(40,71)(41,75)(42,76)(43,73)(44,74)(45,80)(46,79)(47,78)(48,77)(53,54)(55,56)(57,59)(58,60)(61,64)(62,63);;
s2 := ( 1, 9)( 2,10)( 3,11)( 4,12)( 5,13)( 6,14)( 7,15)( 8,16)(17,25)(18,26)(19,27)(20,28)(21,29)(22,30)(23,31)(24,32)(33,41)(34,42)(35,43)(36,44)(37,45)(38,46)(39,47)(40,48)(49,57)(50,58)(51,59)(52,60)(53,61)(54,62)(55,63)(56,64)(65,73)(66,74)(67,75)(68,76)(69,77)(70,78)(71,79)(72,80);;
s3 := ( 3, 4)( 7, 8)( 9,13)(10,14)(11,16)(12,15)(19,20)(23,24)(25,29)(26,30)(27,32)(28,31)(35,36)(39,40)(41,45)(42,46)(43,48)(44,47)(51,52)(55,56)(57,61)(58,62)(59,64)(60,63)(67,68)(71,72)(73,77)(74,78)(75,80)(76,79);;
s4 := ( 2, 4)( 5,13)( 6,16)( 7,15)( 8,14)(10,12)(18,20)(21,29)(22,32)(23,31)(24,30)(26,28)(34,36)(37,45)(38,48)(39,47)(40,46)(42,44)(50,52)(53,61)(54,64)(55,63)(56,62)(58,60)(66,68)(69,77)(70,80)(71,79)(72,78)(74,76);;
poly := Group([s0,s1,s2,s3,s4]);;
Finitely Presented Group Representation (GAP) 
F := FreeGroup("s0","s1","s2","s3","s4");;
s0 := F.1;;  s1 := F.2;;  s2 := F.3;;  s3 := F.4;;  s4 := F.5;;  
rels := [ s0*s0, s1*s1, s2*s2, s3*s3, s4*s4, s0*s2*s0*s2, 
s0*s3*s0*s3, s1*s3*s1*s3, s0*s4*s0*s4, 
s1*s4*s1*s4, s2*s4*s2*s4, s3*s4*s3*s4*s3*s4, 
s0*s1*s2*s1*s0*s1*s2*s1, s1*s2*s1*s2*s1*s2*s1*s2, 
s2*s3*s2*s3*s2*s3*s2*s3, s4*s2*s3*s4*s2*s3*s4*s2*s3, 
s3*s1*s2*s3*s1*s2*s3*s1*s2*s3*s1*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)!( 1,17)( 2,18)( 3,19)( 4,20)( 5,22)( 6,21)( 7,24)( 8,23)( 9,27)(10,28)(11,25)(12,26)(13,32)(14,31)(15,30)(16,29)(33,65)(34,66)(35,67)(36,68)(37,70)(38,69)(39,72)(40,71)(41,75)(42,76)(43,73)(44,74)(45,80)(46,79)(47,78)(48,77)(53,54)(55,56)(57,59)(58,60)(61,64)(62,63);
s2 := Sym(80)!( 1, 9)( 2,10)( 3,11)( 4,12)( 5,13)( 6,14)( 7,15)( 8,16)(17,25)(18,26)(19,27)(20,28)(21,29)(22,30)(23,31)(24,32)(33,41)(34,42)(35,43)(36,44)(37,45)(38,46)(39,47)(40,48)(49,57)(50,58)(51,59)(52,60)(53,61)(54,62)(55,63)(56,64)(65,73)(66,74)(67,75)(68,76)(69,77)(70,78)(71,79)(72,80);
s3 := Sym(80)!( 3, 4)( 7, 8)( 9,13)(10,14)(11,16)(12,15)(19,20)(23,24)(25,29)(26,30)(27,32)(28,31)(35,36)(39,40)(41,45)(42,46)(43,48)(44,47)(51,52)(55,56)(57,61)(58,62)(59,64)(60,63)(67,68)(71,72)(73,77)(74,78)(75,80)(76,79);
s4 := Sym(80)!( 2, 4)( 5,13)( 6,16)( 7,15)( 8,14)(10,12)(18,20)(21,29)(22,32)(23,31)(24,30)(26,28)(34,36)(37,45)(38,48)(39,47)(40,46)(42,44)(50,52)(53,61)(54,64)(55,63)(56,62)(58,60)(66,68)(69,77)(70,80)(71,79)(72,78)(74,76);
poly := sub<Sym(80)|s0,s1,s2,s3,s4>;
Finitely Presented Group Representation (Magma) 
poly<s0,s1,s2,s3,s4> := Group< s0,s1,s2,s3,s4 | s0*s0, s1*s1, s2*s2, 
s3*s3, s4*s4, s0*s2*s0*s2, s0*s3*s0*s3, 
s1*s3*s1*s3, s0*s4*s0*s4, s1*s4*s1*s4, 
s2*s4*s2*s4, s3*s4*s3*s4*s3*s4, s0*s1*s2*s1*s0*s1*s2*s1, 
s1*s2*s1*s2*s1*s2*s1*s2, s2*s3*s2*s3*s2*s3*s2*s3, 
s4*s2*s3*s4*s2*s3*s4*s2*s3, s3*s1*s2*s3*s1*s2*s3*s1*s2*s3*s1*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.