Geodesic
The Simplicial Helix and the Equation tan nθ = n tan θ
Canadian mathematical bulletin, Tome 28 (1985) no. 4, pp. 385-393

Voir la notice de l'article provenant de la source Cambridge University Press

Buckminster Fuller has coined the name tetrahelix for a column of regular tetrahedra, each sharing two faces with neighbours, one 'below' and one 'above' [A. H. Boerdijk, Philips Research Reports 7 (1952), p. 309]. Such a column could well be employed in architecture, because it is both strong and attractive. The (n — 1)-dimensional analogue is based on a skew polygon such that every n consecutive vertices belong to a regular simplex. The generalized twist which shifts this polygon one step along itself is found to have the characteristic equation(λ - 1)2{(n - 1)λn-2 + 2(n - 2)λn-3 + 3(n - 3)λn-4 + . . . + (n - 2)2λ + (n - 1)} = 0,which can be derived from tan nθ = n tan θ by setting λ = exp (2θi).
DOI : 10.4153/CMB-1985-045-5
Mots-clés : S1N20, S1M20, 10A32, Chebyshev polynomial, Petrie polygon, Simplex, Tetrahelix, Cross polytope, Regular polytope, Spherical space, Twist 
Coxeter, H. S. M. The Simplicial Helix and the Equation tan nθ = n tan θ. Canadian mathematical bulletin, Tome 28 (1985) no. 4, pp. 385-393. doi: 10.4153/CMB-1985-045-5
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