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

Small Group ID = [648,610], hypertope number 2.

• Structure of Group

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

• Generators of Automorphism Group (Permutation Representation for GAP)

r0 := (2,4)(5,8)(6,9)(7,14)(10,21)(11,18)(12,25)(13,20)(15,29)(16,30)(17,35)(19,38)(22,41)(23,27)(24,37)(26,33)(28,40)(31,49)(32,47)(34,48)(36,51)(39,44)(42,52)(43,46)(45,50)(53,54);

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

r2 := (2,5)(4,8)(6,13)(7,15)(9,20)(10,21)(11,24)(12,22)(14,29)(16,34)(18,37)(25,41)(26,45)(28,32)(30,48)(31,49)(33,50)(40,47);

r3 := (1,3)(2,6)(4,9)(5,11)(7,16)(8,18)(10,22)(12,26)(13,28)(14,30)(15,32)(17,36)(19,39)(20,40)(21,41)(23,43)(24,34)(25,33)(27,46)(29,47)(31,50)(35,51)(37,48)(38,44)(42,54)(45,49)(52,53);

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

• Number of Elements of each type

type 0: 3 elements

type 1: 27 elements

type 2: 18 elements

type 3: 18 elements

• Order of r₀ r₁ r₂ r₃ : 6

• This hypertope does not have non-degenerate leaves