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

Overview

Group: SmallGroup(960,6310)
Rank: 3
Schläfli Type: {30,4}
Vertices, edges, …: 120, 240, 16
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
Self-Petrie

Quotients maximal quotients in bold

4-fold

{30,4}*240b

5-fold

{6,4}*192a

8-fold

{15,4}*120

20-fold

{6,4}*48c

40-fold

{3,4}*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)^15> of order 2

10 facets

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

60 vertex figures

60 of {4}*8

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

8 facets

8 of {30}*60

60 vertex figures

60 of {4}*8

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

8 facets

8 of {30}*60

70 vertex figures

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

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

4 facets

4 of {30}*60

40 vertex figures

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

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

4 facets

4 of {30}*60

45 vertex figures

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

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

6 facets

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

30 vertex figures

30 of {4}*8

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