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

Small Group ID = [256,7703], hypertope number 1.

• Structure of Group

(C2 x C2 x C2 x C2 x D8) : C2

• Generators of Automorphism Group (Permutation Representation for GAP)

r0 := (1,2)(3,9)(4,7)(5,8)(6,16)(10,22)(11,23)(12,25)(13,19)(14,29)(15,20)(17,32)(18,34)(21,31)(24,40)(26,43)(27,45)(28,35)(30,36)(33,51)(37,49)(38,41)(39,50)(42,56)(44,58)(46,59)(47,60)(48,52)(53,57)(54,55)(61,64)(62,63);

r1 := (1,3)(2,6)(4,12)(5,14)(7,18)(8,11)(9,21)(10,15)(13,27)(16,31)(17,20)(19,26)(22,39)(23,41)(24,36)(25,37)(28,47)(29,38)(30,33)(32,50)(34,49)(35,42)(40,55)(43,57)(44,52)(45,53)(46,48)(51,54)(56,64)(58,63)(59,62)(60,61);

r2 := (1,4)(2,7)(3,10)(5,15)(6,17)(8,20)(9,22)(11,18)(12,14)(13,28)(16,32)(19,35)(21,37)(23,34)(24,42)(25,29)(26,44)(27,46)(30,48)(31,49)(33,47)(36,52)(38,39)(40,56)(41,50)(43,58)(45,59)(51,60)(53,61)(54,62)(55,63)(57,64);

r3 := (1,5)(2,8)(3,11)(4,13)(6,14)(7,19)(9,23)(10,24)(12,26)(15,30)(16,29)(17,33)(18,27)(20,36)(21,38)(22,40)(25,43)(28,48)(31,41)(32,51)(34,45)(35,52)(37,53)(39,54)(42,46)(44,47)(49,57)(50,55)(56,59)(58,60)(61,62)(63,64);

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

• Number of Elements of each type

type 0: 4 elements

type 1: 16 elements

type 2: 8 elements

type 3: 8 elements

• Order of r₀ r₁ r₂ r₃ : 4

• This hypertope does not have non-degenerate leaves