Polytope of Type {4,30} with group SmallGroup(960,6310)

Overview

Group: SmallGroup(960,6310)
Rank: 3
Schläfli Type: {4,30}
Vertices, edges, …: 16, 240, 120
Order of s₀s₁s₂: 30
Order of s₀s₁s₂s₁: 4
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}*240b

5-fold

{4,6}*192a

8-fold

{4,15}*120

20-fold

{4,6}*48c

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=<(s1*s2)^15> of order 2

60 facets

60 of {4}*8

10 vertex figures

4 of {15}*30
6 of {30}*60

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

60 facets

60 of {4}*8

8 vertex figures

8 of {30}*60

P/N, where N=<s0*s2*s1*s0*s1*s2> of order 2

70 facets

50 of {4}*8
20 of {2}*4

8 vertex figures

8 of {30}*60

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

40 facets

20 of {2}*4
20 of {4}*8

4 vertex figures

4 of {30}*60

P/N, where N=<s0*s2*s1*s0*s1*s2, s1*s0*s2*s1*s0*s1*s2*s1> of order 4

45 facets

15 of {4}*8
30 of {2}*4

4 vertex figures

4 of {30}*60

P/N, where N=<(s0*s2*s1)^2*s0*(s1*s2)^2, (s1*s2)^15> of order 4

30 facets

30 of {4}*8

6 vertex figures

4 of {15}*30
2 of {30}*60

Representations

Permutation Representation (GAP)

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

References

None.

to this polytope.