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

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

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

r2 := (2,4)(3,7)(5,10)(8,14)(17,22)(21,26)(23,28)(27,31)(33,37)(38,40);

r3 := (2,5)(3,8)(4,10)(7,14)(17,23)(21,27)(22,28)(26,31)(33,38)(37,40);

• Finitely Presented Group Representation (GAP)

F := FreeGroup(4);

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

G := F/[ r0^2, r2^2, r3^2, r1^2, (r2*r3)^2, (r0*r3)^2, (r0*r2)^2, (r1*r3)^4, (r1*r2*r1*r3)^2, (r1*r2)^4, (r1*r0*r1*r3)^2, (r1*r0*r1*r2)^2, (r1*r0)^10 ];;

• Number of Elements of each type

type 0: 10 elements

type 1: 40 elements

type 2: 4 elements

type 3: 4 elements

• Order of r₀ r₁ r₂ r₃ : 20

• This hypertope does not have non-degenerate leaves