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

Small Group ID = [648,269], 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)(18,22)(24,28)(26,30)(31,35)(33,37)(39,44)(40,45)(42,47)(43,48)(49,52)(50,53)(51,54);

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

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

r3 := (1,4)(2,6)(3,8)(5,12)(7,15)(9,13)(10,18)(11,19)(14,22)(16,24)(17,25)(20,28)(21,29)(23,32)(26,33)(27,36)(30,37)(31,39)(34,41)(35,44)(38,46)(40,47)(42,45)(43,51)(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, (r0*r3)^2, (r0*r2)^2, (r3*r1)^3, (r2*r1)^3, (r0*r1)^4, (r0*r2*r1)^3, (r0*r3*r1)^3, r0*r1*r2*r3*r1*r2*r0*r1*r3*r1*r2*r1*r3*r2, (r3*r2*r1)^6 ];;

• Number of Elements of each type

type 0: 4 elements

type 1: 18 elements

type 2: 27 elements

type 3: 27 elements

• Order of r₀ r₁ r₂ r₃ : 12

• This hypertope does not have non-degenerate leaves