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

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)(16,20)(17,21)(18,22)(23,27)(24,28)(26,30)(32,35)(38,41)(43,46)(45,48)(49,52)(50,53)(51,54);

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

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

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

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

• Number of Elements of each type

type 0: 4 elements

type 1: 54 elements

type 2: 27 elements

type 3: 27 elements

• Order of r₀ r₁ r₂ r₃ : 12

• This hypertope does not have non-degenerate leaves