Polytope of Type {10,10,2}

Atlas Canonical Name {10,10,2}*1000

Overview

Group: SmallGroup(1000,106)
Rank: 4
Schläfli Type: {10,10,2}
Vertices, edges, …: 25, 125, 25, 2
Order of s₀s₁s₂s₃: 10
Order of s₀s₁s₂s₃s₂s₁: 2
Also known as: if this polytope has a name.

Special Properties

Degenerate
Universal
Non-Orientable
Flat

Quotients maximal quotients in bold

No regular quotients.

Covers minimal covers in bold

2-fold

{10,10,2}*2000c

Representations

Permutation Representation (GAP)

s0 := ( 2, 5)( 3, 4)( 6,21)( 7,25)( 8,24)( 9,23)(10,22)(11,16)(12,20)(13,19)(14,18)(15,17);;
s1 := ( 1, 6)( 2, 7)( 3, 8)( 4, 9)( 5,10)(11,21)(12,22)(13,23)(14,24)(15,25);;
s2 := ( 2, 5)( 3, 4)( 6, 7)( 8,10)(11,13)(14,15)(16,19)(17,18)(21,25)(22,24);;
s3 := (26,27);;
poly := Group([s0,s1,s2,s3]);;

Finitely Presented Group Representation (GAP)

F := FreeGroup("s0","s1","s2","s3");;
s0 := F.1;;  s1 := F.2;;  s2 := F.3;;  s3 := F.4;;  
rels := [ s0*s0, s1*s1, s2*s2, s3*s3, s0*s2*s0*s2, 
s0*s3*s0*s3, s1*s3*s1*s3, s2*s3*s2*s3, 
s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1*s2, 
s0*s1*s2*s1*s0*s1*s2*s1*s2*s1*s0*s1*s2*s1*s0*s1 ];;
poly := F / rels;;

Permutation Representation (Magma)

s0 := Sym(27)!( 2, 5)( 3, 4)( 6,21)( 7,25)( 8,24)( 9,23)(10,22)(11,16)(12,20)(13,19)(14,18)(15,17);
s1 := Sym(27)!( 1, 6)( 2, 7)( 3, 8)( 4, 9)( 5,10)(11,21)(12,22)(13,23)(14,24)(15,25);
s2 := Sym(27)!( 2, 5)( 3, 4)( 6, 7)( 8,10)(11,13)(14,15)(16,19)(17,18)(21,25)(22,24);
s3 := Sym(27)!(26,27);
poly := sub<Sym(27)|s0,s1,s2,s3>;

Finitely Presented Group Representation (Magma)

poly<s0,s1,s2,s3> := Group< s0,s1,s2,s3 | s0*s0, s1*s1, s2*s2, 
s3*s3, s0*s2*s0*s2, s0*s3*s0*s3, s1*s3*s1*s3, 
s2*s3*s2*s3, s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1*s2, 
s0*s1*s2*s1*s0*s1*s2*s1*s2*s1*s0*s1*s2*s1*s0*s1 >;