Polytope of Type {10,6} with group SmallGroup(960,10891)

Overview

Group: SmallGroup(960,10891)
Rank: 3
Schläfli Type: {10,6}
Vertices, edges, …: 80, 240, 48
Order of s₀s₁s₂: 10
Order of s₀s₁s₂s₁: 20
Also known as: if this polytope has a name.

Special Properties

Compact Hyperbolic Quotient
Locally Spherical
Orientable
Self-Petrie

Quotients maximal quotients in bold

2-fold

{10,6}*480c

4-fold

8-fold

16-fold

{5,3}*60

120-fold

{2,2}*8

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)^5> of order 2

36 facets

24 of {5}*10
12 of {10}*20

40 vertex figures

40 of {6}*12

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

24 facets

24 of {10}*20

60 vertex figures

20 of {6}*12
40 of {3}*6

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

24 facets

24 of {10}*20

40 vertex figures

40 of {6}*12

P/N, where N=<s0*s1*s2*(s1*s0)^3*s1*s2*s1> of order 3

16 facets

16 of {10}*20

32 vertex figures

24 of {6}*12
8 of {2}*4

Representations

Permutation Representation (GAP)

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

Permutation Representation (Magma)

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

References

None.

to this polytope.