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

Small Group ID = [648,610], hypertope number 1.

• Structure of Group

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

• Generators of Automorphism Group (Permutation Representation for GAP)

r0 := (2,3)(4,7)(5,8)(6,13)(9,20)(10,17)(11,23)(12,19)(14,26)(15,27)(16,32)(18,35)(21,24)(22,34)(28,36)(29,40)(30,38)(31,42)(33,46)(37,49)(39,45)(41,47)(43,48)(44,51)(50,52)(53,54);

r1 := (1,2)(3,6)(4,9)(5,11)(7,16)(8,18)(10,21)(12,24)(13,25)(14,28)(15,30)(17,31)(19,29)(20,36)(22,37)(23,38)(26,39)(27,41)(32,45)(33,34)(35,47)(40,50)(42,52)(43,44)(46,53)(48,49)(51,54);

r2 := (2,4)(3,7)(5,12)(6,14)(8,19)(9,20)(10,22)(11,23)(13,26)(15,31)(17,34)(18,33)(21,24)(27,42)(29,44)(30,43)(35,46)(37,49)(38,48)(39,45)(40,51)(41,47)(50,52)(53,54);

r3 := (2,5)(3,8)(4,10)(6,15)(7,17)(9,20)(11,23)(12,22)(13,27)(14,29)(16,33)(19,34)(21,24)(26,40)(28,43)(31,44)(32,46)(36,48)(37,49)(39,45)(41,47)(42,51)(50,52)(53,54);

• 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, (r3*r0)^2, (r2*r0)^2, (r2*r3)^3, ((r1*r2)^2*r0)^2, (r3*(r1*r2)^2)^2, r1*r3*r1*r2*r0*(r1*r3)^2*r2*r3*r0, ((r1*r0)^2*r1*r2)^2, (r1*r0)^6 ];;

• 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