Polytope of Type {8,30} with group SmallGroup(960,6311)

Overview

Group: SmallGroup(960,6311)
Rank: 3
Schläfli Type: {8,30}
Vertices, edges, …: 16, 240, 60
Order of s₀s₁s₂: 15
Order of s₀s₁s₂s₁: 8
Also known as: if this polytope has a name.

Special Properties

Compact Hyperbolic Quotient
Locally Spherical
Non-Orientable

Quotients maximal quotients in bold

4-fold

{4,30}*240c

5-fold

{8,6}*192a

8-fold

{4,15}*120

20-fold

{4,6}*48b

40-fold

{4,3}*24

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=<(s0*s1)^4> of order 2

40 facets

20 of {4}*8
20 of {8}*16

8 vertex figures

8 of {30}*60

Representations

Permutation Representation (GAP)

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

Finitely Presented Group Representation (GAP)

F := FreeGroup("s0","s1","s2");;
s0 := F.1;;  s1 := F.2;;  s2 := F.3;;  
rels := [ s0*s0, s1*s1, s2*s2, s0*s2*s0*s2, s0*s1*s2*s0*s1*s2*s0*s1*s0*s1*s2*s0*s1*s2*s0*s1, 
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1, 
s2*s1*s0*s1*s2*s1*s0*s1*s2*s0*s1*s0*s1*s2*s1*s0*s1*s0, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s0*s2*s1*s0*s2*s1*s0*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 ];;
poly := F / rels;;

Permutation Representation (Magma)

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

Finitely Presented Group Representation (Magma)

poly<s0,s1,s2> := Group< s0,s1,s2 | s0*s0, s1*s1, s2*s2, 
s0*s2*s0*s2, s0*s1*s2*s0*s1*s2*s0*s1*s0*s1*s2*s0*s1*s2*s0*s1, 
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1, 
s2*s1*s0*s1*s2*s1*s0*s1*s2*s0*s1*s0*s1*s2*s1*s0*s1*s0, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s0*s2*s1*s0*s2*s1*s0*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 >;

References

None.

to this polytope.