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

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

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

r2 := (2,4)(3,7)(5,12)(6,14)(8,19)(9,20)(10,23)(11,21)(13,27)(15,32)(17,34)(24,37)(28,43)(30,44)(40,45)(41,51)(42,49)(47,53);

r3 := (2,5)(3,8)(4,10)(6,15)(7,17)(9,21)(11,24)(12,23)(13,28)(14,30)(19,34)(20,37)(27,41)(32,44)(40,49)(42,47)(43,51)(45,53);

• Finitely Presented Group Representation (GAP)

F := FreeGroup(4);

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

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