Geodesic
A modification of the Fourier--Motskin algorithm for constructing a~triangulation and its star coloring
Diskretnyj analiz i issledovanie operacij, Tome 13 (2006) no. 1, pp. 77-94.

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The notion of a star development of a simplicial complex is introduced, and an algorithm is offered that simultaneously constructs a triangulation and a star development of the simplicial complex of the faces of the triangulation for a point configuration in general position. 
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V. N. Shevchenko; D. V. Gruzdev. A modification of the Fourier--Motskin algorithm for constructing a~triangulation and its star coloring. Diskretnyj analiz i issledovanie operacij, Tome 13 (2006) no. 1, pp. 77-94. http://geodesic.mathdoc.fr/item/DA_2006_13_1_a5/

[1] Akho A., Khopkroft Dzh., Ulman Dzh., Postroenie i analiz vychislitelnykh algoritmov, Mir, M., 1979 | MR | Zbl

[2] Brensted A., Vvedenie v teoriyu vypuklykh mnogogrannikov, Mir, M., 1988 | MR

[3] Emelichev V. A., Kovalev M. M., Kravtsov M. K., Mnogogranniki, grafy, optimizatsiya, Nauka, M., 1981 | MR

[4] Motskin T. S., Raifa Kh., Tompson Dzh. L., Troll R. M., “Metod dvoinogo opisaniya”, Matrichnye igry, Fizmatgiz, M., 1961, 81–109

[5] Pontryagin L. S., Osnovy kombinatornoi topologii, OGIZ, M., 1947 | MR

[6] Preparata F., Sheimos M., Vychislitelnaya geometriya: Vvedenie, Mir, M., 1989 | MR | Zbl

[7] Chernikov S. N., Lineinye neravenstva, Nauka, M., 1968 | MR | Zbl

[8] Shevchenko V. N., “O maksimalnykh triangulyatsiyakh vypuklykh politopov”, Mezhdunarodnaya konferentsiya “Diskretnyi analiz i issledovanie operatsii”, Materialy konferentsii (Novosibirsk, 26 iyunya–1 iyulya 2000), Izd-vo In-ta matematiki, Novosibirsk, 2000, 163

[9] Shevchenko V. N., Gruzdev D. V., “Modifikatsiya algoritma Fure–Motskina dlya postroeniya triangulyatsii i ee razvertki”, Materialy XIII Mezhdunarodnoi shkoly-seminara “Sintez i slozhnost upravlyayuschikh sistem”, Chast I (Penza, 14–20 oktyabrya 2002 g.), Izd-vo tsentra prikladnykh issledovanii pri mekhaniko-matematicheskom fakultete MGU, M., 2002, 200–205

[10] Shevchenko V. N., Gruzdev D. V., “Modifikatsiya algoritma Fure–Motskina dlya postroeniya triangulyatsii”, Diskret. analiz i issled. operatsii. Ser. 2, 10:1 (2003), 53–64 | MR | Zbl

[11] Bruggesser H., Mani P., “Shellable decompositions of cells and spheres”, Math. Scand., 29 (1971), 197–205 | MR

[12] Burger E., “Über homogene lineare Ungleichungssysteme”, Zeitschrift Angewandte Math. und Mech., 36 (1956), 135–139 | DOI | MR | Zbl

[13] Grünbaum B., Convex polytopes, Wiley, N.Y., 1967 | MR | Zbl

[14] Lee C. W., “Regular triangulations of convex polytopes”, Applied geometry and discrete mathematics, DIMACS Series in Discrete Mathematics and Theoretical Computer Science, 4, Amer. Math. Soc., Providence, RI, 1991, 443–456 | MR

[15] Rudin M. E., “An unshellable triangulation of a tetrahedron”, Bulletin Amer. Math. Soc., 64 (1958), 90–91 | DOI | MR | Zbl

[16] Ziegler G. I., Lectures on convex polytopes, Springer-Verlag, Berlin, 1994