Rank 4 Tail-triangle diagram with parameters (a,b,c,d) = (4,9,3,3)

Small Group ID = [648,281], hypertope number 1.

• Structure of Group

((C2 x C2) : ((C3 x C3 x C3) : C3)) : C2

• Generators of Automorphism Group (Permutation Representation for GAP)

r0 := (1,2)(3,5)(4,6)(8,12)(10,14)(16,18);

r1 := (3,7)(4,9)(5,11)(6,13)(8,10)(12,14)(15,16)(17,18);

r2 := (1,3)(2,5)(4,10)(6,14)(7,15)(8,16)(11,17)(12,18);

r3 := (1,4)(2,6)(3,8)(5,12)(7,15)(10,16)(11,17)(14,18);

• Finitely Presented Group Representation (GAP)

F := FreeGroup(4);

r0 := F.1;; r1 := F.2;; r2 := F.3;; r3 := F.4;;

G := F/[ r0^2, r2^2, r3^2, r1^2, (r2*r0)^2, (r3*r0)^2, (r2*r3)^3, (r1*r3)^3, (r1*r0)^4, (r1*r3*r0)^3, r1*r0*r2*r1*r0*r1*r2*r1*r0, (r1*r2*r1*r3)^2*r2*r1*r2*r3, (r1*r2*r3*r2*r1*r2)^3 ];;

• Number of Elements of each type

type 0: 4 elements

type 1: 54 elements

type 2: 27 elements

type 3: 9 elements

• Order of r₀ r₁ r₂ r₃ : 12

• This hypertope does not have non-degenerate leaves