Rank 4 Tail-triangle diagram with parameters (a,b,c,d) = (6,4,3,4)

Small Group ID = [288,1028], hypertope number 1.

• Structure of Group

C2 x S4 x S3

• Generators of Automorphism Group (Permutation Representation for GAP)

r0 := (2,4)(5,8)(6,9)(10,14)(11,15)(16,18);

r1 := (1,2)(3,6)(5,9)(7,11)(8,13)(10,15)(12,16)(14,17);

r2 := (3,7)(5,10)(8,14);

r3 := (1,3)(2,5)(4,8)(6,9)(7,12)(10,16)(11,15)(14,18);

• Finitely Presented Group Representation (GAP)

F := FreeGroup(4);

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

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

• Number of Elements of each type

type 0: 6 elements

type 1: 18 elements

type 2: 8 elements

type 3: 6 elements

• Order of r₀ r₁ r₂ r₃ : 6

• This hypertope does not have non-degenerate leaves