Polytope of Type {15,15} with group SmallGroup(1920,240395)

Overview

Group: SmallGroup(1920,240395)
Rank: 3
Schläfli Type: {15,15}
Vertices, edges, …: 64, 480, 64
Order of s₀s₁s₂: 4
Order of s₀s₁s₂s₁: 15
Also known as: if this polytope has a name.

Special Properties

Compact Hyperbolic Quotient
Locally Spherical
Orientable
Self-Dual

Quotients maximal quotients in bold

12-fold

{5,5}*160

80-fold

{3,3}*24

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=<(s0*s1)^3*s0*s2*(s1*s0)^2*s1*s2> of order 2

32 facets

32 of {15}*30

32 vertex figures

32 of {15}*30

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

32 facets

32 of {15}*30

32 vertex figures

32 of {15}*30

Representations

Permutation Representation (GAP)

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

Permutation Representation (Magma)

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

References

None.

to this polytope.