Rank 4 Tail-triangle diagram with parameters (a,b,c,d) = (4,3,9,3)

Small Group ID = [648,274], hypertope number 1.

• Structure of Group

((C2 x C2) : ((C9 x C3) : C3)) : C2

• Generators of Automorphism Group (Permutation Representation for GAP)

r0 := (1,2)(3,5)(4,6)(8,12)(10,14)(16,22)(17,23)(20,26)(28,35)(29,36)(31,38)(33,40)(41,47)(42,48)(44,50)(45,51)(46,52)(53,54);

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

r2 := (1,3)(2,5)(4,10)(6,14)(7,11)(8,17)(9,18)(12,23)(13,24)(15,27)(16,28)(19,32)(20,29)(21,34)(22,35)(25,39)(26,36)(30,43)(31,44)(33,41)(37,49)(38,50)(40,47)(42,51)(45,48)(46,53)(52,54);

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

• 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, (r0*r2)^2, (r2*r3)^3, (r2*r1)^3, (r1*r0)^4, (r1*r2*r0)^3, r3*(r1*r0)^2*r3*r1*r0*r1, r2*r1*r3*r2*r1*r2*r3*r0*r2*r1*r2*r3*r1*r0, r3*r1*r2*(r1*r3)^2*r1*(r2*r1*r3)^2*r1*r2, (r1*r3*r2)^6 ];;

• Number of Elements of each type

type 0: 4 elements

type 1: 54 elements

type 2: 9 elements

type 3: 27 elements

• Order of r₀ r₁ r₂ r₃ : 12

• This hypertope does not have non-degenerate leaves