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

Small Group ID = [648,732], hypertope number 2.

• Structure of Group

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

• Generators of Automorphism Group (Permutation Representation for GAP)

r0 := (1,2)(3,6)(4,7)(5,11)(8,18)(9,15)(10,17)(12,23)(13,20)(14,25)(16,28)(19,30)(21,29)(22,33)(24,32)(26,31)(27,34)(35,36);

r1 := (2,5)(3,8)(4,10)(6,14)(7,16)(9,20)(11,22)(12,24)(13,17)(15,27)(18,29)(19,31)(21,32)(23,25)(28,34)(30,35);

r2 := (1,3)(2,6)(4,10)(5,12)(7,17)(9,20)(11,23)(13,15)(14,24)(16,27)(19,31)(21,22)(25,32)(26,30)(28,34)(29,33);

r3 := (1,4)(2,7)(3,9)(5,13)(6,15)(8,19)(10,21)(11,20)(12,16)(14,26)(17,29)(18,30)(22,34)(23,28)(24,35)(25,31)(27,33)(32,36);

• Finitely Presented Group Representation (GAP)

F := FreeGroup(4);

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

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

• Number of Elements of each type

type 0: 6 elements

type 1: 27 elements

type 2: 9 elements

type 3: 18 elements

• Order of r₀ r₁ r₂ r₃ : 6

• This hypertope does not have non-degenerate leaves