Rank 4 Star diagram with parameters (a,b,c) = (8,4,4)

Small Group ID = [256,25866], 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)(3,5)(4,7)(6,10)(8,13)(9,15)(11,14)(12,17)(16,20)(18,22)(19,23)(21,25)(24,28)(26,30)(27,29)(31,32);

r1 := (1,3)(2,4)(5,9)(6,11)(7,12)(8,14)(10,16)(13,18)(15,19)(17,21)(20,24)(22,26)(23,27)(25,29)(28,31)(30,32);

r2 := (3,4)(5,7)(6,8)(10,13)(19,21)(23,25)(24,26)(28,30);

r3 := (3,6)(4,8)(5,10)(7,13)(19,24)(21,26)(23,28)(25,30);

• Finitely Presented Group Representation (GAP)

F := FreeGroup(4);

r0 := F.1;; r1 := F.2;; r2 := F.3;; r3 := F.4;;

G := F/[ r2^2, r3^2, r0^2, r1^2, (r2*r0)^2, (r0*r3)^2, (r2*r3)^2, (r3*r1*r2*r1)^2, (r2*r1)^4, (r1*r3)^4, (r1*r0*r1*r3)^2, (r1*r2*r1*r0)^2, (r0*r1)^8 ];;

• Number of Elements of each type

type 0: 8 elements

type 1: 32 elements

type 2: 4 elements

type 3: 4 elements

• Order of r₀ r₁ r₂ r₃ : 8

• This hypertope does not have non-degenerate leaves