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

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)(17,23)(18,24)(20,26)(27,34)(29,36)(31,38)(33,40)(41,47)(42,48)(43,49)(45,51)(46,52)(53,54);

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

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

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

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

• Number of Elements of each type

type 0: 4 elements

type 1: 54 elements

type 2: 27 elements

type 3: 9 elements

• Order of r₀ r₁ r₂ r₃ : 12

• This hypertope does not have non-degenerate leaves