Regular dodecahedron

NP

Published in J.-P. Barthelemy, G. Cohen, A. Lobstein, Catherine Fritsch-Mignotte, Maurice Mignotte, Algorithmic Complexity and communication problems, 2020

J.-P. Barthelemy, G. Cohen, A. Lobstein

The problem, initially given by Hamilton, was the trip around the earth: consider twenty cities on the globe and suppose that these cities are the vertices of a regular dodecahedron. How can a traveller go once, and only once, through each city and come back to the departure point (the roads between the cities are the edges of the dodecahedron)? The elegant solution given by Hamilton made use of the structure of the regular dodecahedron (cf.Berge, 1973, p. 179). When the dodecahedron is replaced by any graph, then we get the problem of the Hamiltonian cycle.

Conjugate heat transfer analysis within in lattice-filled heat exchanger for additive manufacturing

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Journal Information

Published in Mechanics of Advanced Materials and Structures, 2022

Nadhir Lebaal, Abdelhakim SettaR, Sebastien Roth, Samuel Gomes

The model of lattice pattern used in this study is called the Dodecahedron network [25]. The geometry of the dodecahedron is a polyhedron with twelve flat faces as shown in Figure 1. The best-known dodecahedron is the regular dodecahedron, which is a platonic solid.

Regular dodecahedron

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Conjugate heat transfer analysis within in lattice-filled heat exchanger for additive manufacturing