Polytope of Type {6,24} with group SmallGroup(576,5053)

Overview

Group: SmallGroup(576,5053)
Rank: 3
Schläfli Type: {6,24}
Vertices, edges, …: 12, 144, 48
Order of s₀s₁s₂: 3
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

3-fold

{6,8}*192a

4-fold

{6,12}*144d

12-fold

{6,4}*48b

24-fold

{3,4}*24

Covers minimal covers in bold

2-fold

3-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*s2*s1)^4> of order 2

24 facets

24 of {6}*12

8 vertex figures

4 of {24}*48
4 of {12}*24

Representations

Permutation Representation (GAP)

s0 := ( 3, 4)( 5,10)( 6, 9)( 7,11)( 8,12)(15,16)(19,20)(21,26)(22,25)(23,27)(24,28)(31,32)(35,36)(37,42)(38,41)(39,43)(40,44)(47,48);;
s1 := ( 2, 3)( 5, 8)( 9,16)(10,14)(11,15)(12,13)(17,33)(18,35)(19,34)(20,36)(21,40)(22,38)(23,39)(24,37)(25,48)(26,46)(27,47)(28,45)(29,44)(30,42)(31,43)(32,41);;
s2 := ( 1,29)( 2,30)( 3,31)( 4,32)( 5,25)( 6,26)( 7,27)( 8,28)( 9,21)(10,22)(11,23)(12,24)(13,17)(14,18)(15,19)(16,20)(33,45)(34,46)(35,47)(36,48)(37,41)(38,42)(39,43)(40,44);;
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*s2, 
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1, 
s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1 ];;
poly := F / rels;;

Permutation Representation (Magma)

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

References

None.

to this polytope.