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

Small Group ID = [648,733], hypertope number 3.

• Structure of Group

((C3 x C3 x C3) : (C2 x C2)) x S3

• Generators of Automorphism Group (Permutation Representation for GAP)

r0 := (1,2)(3,5)(4,6)(7,15)(8,12)(9,18)(10,14)(11,20)(13,23)(16,24)(17,22)(19,21);

r1 := (1,2)(3,7)(4,9)(5,11)(6,13)(8,17)(10,12)(14,22)(15,20)(16,24)(18,23)(19,21);

r2 := (1,3)(2,5)(4,10)(6,14)(7,16)(8,18)(9,12)(11,21)(13,22)(15,24)(17,23)(19,20);

r3 := (1,4)(2,6)(3,8)(5,12)(7,14)(9,19)(10,15)(11,22)(13,24)(16,23)(17,20)(18,21);

• Finitely Presented Group Representation (GAP)

F := FreeGroup(4);

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

G := F/[ r0^2, r1^2, r2^2, r3^2, (r0*r3)^2, (r0*r2)^2, (r1*r0)^3, (r2*r1)^6, r1*r2*r3*r2*r1*r3*r0*r1*r3*r1*r2*r3*r2*r0, (r2*r3*r1*r3*r2*r1*r3*r0)^2, r1*r0*r2*(r3*r1)^2*r0*r1*r2*r3*(r2*r1)^2*r3, r2*r1*r3*r2*(r3*r1)^2*(r2*r1)^2*r2*r3*r2*r1, r3*r2*r3*(r1*r2*r0)^2*r3*r2*r3*(r2*r0*r1)^2, (r3*r1*r2*r0*r3*r2)^3 ];;

• Number of Elements of each type

type 0: 3 elements

type 1: 27 elements

type 2: 18 elements

type 3: 18 elements

• Order of r₀ r₁ r₂ r₃ : 6

• This hypertope does not have non-degenerate leaves