Polytope of Type {15,4,4} with group SmallGroup(960,6310)

Overview

Group: SmallGroup(960,6310)
Rank: 4
Schläfli Type: {15,4,4}
Vertices, edges, …: 15, 60, 16, 8
Order of s₀s₁s₂s₃: 30
Order of s₀s₁s₂s₃s₂s₁: 4
Also known as: if this polytope has a name.

Special Properties

Universal
Non-Orientable
Flat

Quotients maximal quotients in bold

4-fold

{15,4,2}*240

5-fold

{3,4,4}*192a

20-fold

{3,4,2}*48

Covers minimal covers in bold

2-fold

Irregular Quotients of which this is a minimal cover

Click an entry to reveal its facets and vertex figures.

P/N, where N=<(s2*s3)^2> of order 2

4 facets

4 of {15,4}*120

15 vertex figures

10 of 2-fold non-regular quotient of {4,4}*64
5 of {4,4}*32

Representations

Permutation Representation (GAP)

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

Permutation Representation (Magma)

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

References

None.

to this polytope.