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

Small Group ID = [288,851], hypertope number 1.

• Structure of Group

GL(2,3) x S3

• Generators of Automorphism Group (Permutation Representation for GAP)

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

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

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

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

• 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, (r2*r0)^2, (r3*r0)^2, (r1*r3)^3, (r2*r1)^3, r3*r2*r1*(r3*r1*r2)^2*r1, r1*r0*r1*r2*r3*r1*r0*r1*r3*r2, r1*r0*r3*r1*r2*r3*r2*r0*r3*r1*r0*r2*r3*r2*r1*r0, r3*(r1*r0)^2*r2*r3*r1*r3*r2*r3*r0*r1*r0*r2*r1 ];;

• Number of Elements of each type

type 0: 6 elements

type 1: 18 elements

type 2: 8 elements

type 3: 8 elements

• Order of r₀ r₁ r₂ r₃ : 24

• This hypertope does not have non-degenerate leaves