Rank 4 Star diagram with parameters (a,b,c) = (4,4,10)

Small Group ID = [320,1260], hypertope number 1.

• Structure of Group

((C2 x C2 x C2 x C2) : C2) x D10

• Generators of Automorphism Group (Permutation Representation for GAP)

r0 := (1,2)(3,5)(4,7)(6,10)(8,13)(9,12)(11,14)(15,17)(16,18)(19,21)(20,23)(22,25)(24,27)(26,29)(28,30)(31,33)(32,34)(35,37)(36,39)(38,40);

r1 := (1,3)(2,4)(5,9)(6,11)(7,12)(8,14)(10,15)(13,17)(16,20)(18,22)(19,23)(21,25)(24,28)(26,30)(27,31)(29,33)(32,36)(34,38)(35,39)(37,40);

r2 := (3,4)(5,7)(6,8)(10,13)(20,22)(23,25)(24,26)(27,29)(36,38)(39,40);

r3 := (3,6)(4,8)(5,10)(7,13)(11,16)(14,18)(15,19)(17,21)(20,24)(22,26)(23,27)(25,29)(28,32)(30,34)(31,35)(33,37);

• 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, (r0*r3)^2, (r0*r2)^2, (r2*r3)^2, (r3*r1*r2*r1)^2, (r2*r1)^4, (r1*r0*r1*r3)^2, (r0*r1)^4, (r1*r2*r1*r0)^2, (r1*r3)^10 ];;

• Number of Elements of each type

type 0: 4 elements

type 1: 40 elements

type 2: 4 elements

type 3: 10 elements

• Order of r₀ r₁ r₂ r₃ : 20

• This hypertope does not have non-degenerate leaves