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

Small Group ID = [648,732], hypertope number 1.

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

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

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

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

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

• 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