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

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

r1 := (1,3)(2,5)(4,10)(6,12)(7,15)(8,18)(9,20)(11,22)(13,25)(14,26)(16,27)(17,29)(19,32)(21,31)(23,33)(24,34)(28,36)(30,35);

r2 := (1,2)(3,8)(4,11)(5,13)(6,15)(7,16)(9,21)(10,19)(12,23)(14,24)(17,30)(18,29)(20,27)(22,28)(25,35)(26,36)(31,33)(32,34);

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

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

• Number of Elements of each type

type 0: 6 elements

type 1: 54 elements

type 2: 9 elements

type 3: 9 elements

• Order of r₀ r₁ r₂ r₃ : 6

• This hypertope does not have non-degenerate leaves