Convex polyhedra with regular faces
Zapiski Nauchnykh Seminarov POMI, Convex polyhedra with regular faces, Tome 2 (1967), pp. 5-221 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice du chapitre de livre

@article{ZNSL_1967_2_a0,
     author = {V. A. Zalgaller},
     title = {Convex polyhedra with regular faces},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {5--221},
     year = {1967},
     volume = {2},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_1967_2_a0/}
}
TY  - JOUR
AU  - V. A. Zalgaller
TI  - Convex polyhedra with regular faces
JO  - Zapiski Nauchnykh Seminarov POMI
PY  - 1967
SP  - 5
EP  - 221
VL  - 2
UR  - http://geodesic.mathdoc.fr/item/ZNSL_1967_2_a0/
LA  - ru
ID  - ZNSL_1967_2_a0
ER  - 
%0 Journal Article
%A V. A. Zalgaller
%T Convex polyhedra with regular faces
%J Zapiski Nauchnykh Seminarov POMI
%D 1967
%P 5-221
%V 2
%U http://geodesic.mathdoc.fr/item/ZNSL_1967_2_a0/
%G ru
%F ZNSL_1967_2_a0
V. A. Zalgaller. Convex polyhedra with regular faces. Zapiski Nauchnykh Seminarov POMI, Convex polyhedra with regular faces, Tome 2 (1967), pp. 5-221. http://geodesic.mathdoc.fr/item/ZNSL_1967_2_a0/

[1] Adamar Zh., Elementarnaya geometriya, ch. II, Uchpedgiz, 1938

[2] Aleksandrov A. D., Vypuklye mnogogranniki, Gostekhizdat, 1950

[3] Ashkinuze V. G., “O chisle polupravilnykh mnogogrannikov”, Matem. prosvesch., no. 1, 1957, 107–118 | Zbl

[4] Grek A. S., “Pravilnye mnogogranniki na zamknutoi poverkhnosti s eilerovoi kharakteristikoi $\chi=-1$”, Tr. Tbilissk. matem. in-ta AN GruzSSR, 27 (1960), 103–112 | Zbl

[5] Gilbert D. i Kon-Fossen S. E., Naglyadnaya geometriya, Gostekhizdat, 1951

[6] Delone B. N., Bolsh. Sov. Ents., izd. 2, 26, 1954, 652–654

[7] Evklid, Nachala, Gostekhizdat, 1950

[8] Zalgaller V. A., “Pravilnogrannye mnogogranniki”, Vestn. Leningr. un-ta, 1963, no. 7, 5–8

[9] Zalgaller V. A. i dr., “O pravilnogrannykh mnogogrannikakh”, Vestn. Leningr. un-ta, 1965, no. I, 150–152 | Zbl

[10] Zalgaller V. A., “Perechen vsekh vypuklykh mnogogrannikov s pravilnymi granyami”, Mezhdunar. kongr. matematikov, Tezisy (sektsiya 9) (Moskva 1966), 28–29

[11] Kenigson V. N., “Analiticheskoe dokazatelstvo teoremy Stringkhema o pravilnykh mnogogrannikakh v $n$-mernom prostranstve”, Tr. Kazakhsk. s.-kh. inst., 9 (1961), 108–24

[12] Koshi O., “Issledovanie o mnogogrannikakh”, Usp. Matem. Nauk, 1944, no. 10, 5–17

[13] Keli A., “O chetyrekh novykh pravilnykh telakh Puanso”, Usp. Matem. Nauk, 1944, no. 10, 18–21

[14] Lyusternik L. A., Vypuklye figury i mnogogranniki, Gostekhizdat, 1956

[15] Nikolskii A., “Polupravilnye tela Arkhimeda”, Matem. v shkole, 1940, no. 5, 5–11

[16] Perepelkin D. I., Kurs elementarnoi geometrii, ch. II, Gostekhizdat, 1949

[17] Rademakher G. i Teplits O., Chisla i figury, “Nauka”, 1966

[18] Sopov S. P., “Ob odnorodnykh mnogogrannikakh s neotritsatelnoi eilerovoi kharakteristikoi”, Mezhdunar. kongr. matematikov, Tezisy (sektsiya 9) (Moskva 1966), 47

[19] Stringkhem V. I., “Pravilnye figury v $n$-mernom prostranstve”, Usp. Matem. Nauk, 1944, no. 10, 22–33

[20] Tot L. F., Raspolozheniya na ploskosti, na sfere i v prostranstve, Fizmatgiz, 1958

[21] Shteingauz G., Matematicheskii kaleidoskop, Gostekhizdat, 1949

[22] ApSimon H. G., “Three facially-regular polyhedra”, Canad. J. Math., 2 (1950), 316–320 | MR

[23] ApSimon H. G., “Two vertex-regular polybedra”, Canad. J. Math., 3 (1951), 269–271 | MR | Zbl

[24] ApSimon H. G., “Almost regular polyhedra”, Math. Gaz., 40:322 (1956), 81–85 | DOI | MR | Zbl

[25] Baker R. P., “Sayley diagrams on the anchor ring”, Am. J. Math., 53 (1931), 645–669 | DOI | MR | Zbl

[26] Bilimovitch A., “Über die Rolle der Archimedischen gleicheckigen Polyeder im $n$-Körperprobleme”, Ac. Serbe Bull. Ac. Sci. Nat., 7 (1941), 197–212 | MR

[27] Bilinski S., “Homogene Netze geschlossener orientierbarer Flächen”, RAD de l'Acad. Yougoslave, 277 (1950), 129–164 | MR

[28] Bilinski S., “Über die Rhombenisoeder”, Glanik mat.-fis. i astr., 15:4 (1960), 251–263 | MR | Zbl

[29] Borrelli F., “I polyedri neoplatonici”, Napoli. Ict. ed. campano, 1959, 1–19

[30] Brückner M., Vielecke und Vielfläche (Theorie and Geschichte), Leipzig, 1900 | Zbl

[31] Cauchy A., “Sur les polygenes et polyédres, second Memoire”, J. de l'Ecole polytechn., 9 (1813), 87

[32] Čech V., “Nĕkt eré poznatky z teorie mnohostĕnụ”, Sb. Ped. inst. Ústínad Labem, Rado math. prirodoved., Praha, 1961, 35–53

[33] Chilton B. L., “On the projection of the regular polytope (5.3.3) into a regular triacontagon”, Canad. Math. Bull., 7:3 (1964), 385–398 | MR | Zbl

[34] Coxeter H. S. M., “The densities of the regular polytopes”, Proc. Cambr. philos. Soc., 27 (1931), 201–211 ; “II”, 28 (1932), 509–521 ; “III”, 29 (1933), 1–22 | DOI | Zbl | DOI | Zbl | DOI | Zbl

[35] Coxeter H. S. M., “The polytopes with regular-prismatic vertex figures, II”, Proc. Lond. math. soc., II s., 34 (1932), 126–189 | DOI | Zbl

[36] Goxeter H. S. M., “Regular compound polytopes in more than four dimensions”, J. math. phys. Massach. Inst. Technol., 12 (1933), 334–345

[37] Coxeter H. S. M., “Withoff's construction for uniform polytopes”, Proc. Lond. math. soc., II s., 38 (1934), 327–339 | DOI | Zbl

[38] Coxeter H. S. M., “Regular skew polyhedra in three and four dimensions, and their topological analogues”, Proc. Lond. math. soc., II s., 43 (1937), 33–62 | DOI | Zbl

[39] Coxeter H. S. M., Val P., Flather H. T., Petrie I. F., “The fifty-nine isocahedra”, Univ. of Toronto, Stud., math. ser., 6 (1938), 1–26

[40] Coxeter H. S. M., “Regular and semi-regular polytopes. I”, Math. Z., 46 (1940), 380–407 | DOI | MR | Zbl

[41] Coxeter H. S. M., “Regular honeycombs in hyperbolic space”, Proc. “Int. Congr. Math. I954”, 3, 1956, 155–169 | MR | Zbl

[42] Coxeter H. S. M., Regular polytopes, N.-Y., 1963 | MR

[43] Coxeter H. S. M., Longuet-Higgins M. S., Miller I. C. P., “Uniform polyhedra”, Philos. trans. Roy. soc. London, ser. A, 246:916 (1954), 401–450 | DOI | MR | Zbl

[44] Cundy H. M., “Deltahedra”, Math. Gesz., 36 (1952), 263–266 | DOI | MR

[45] Cundy H. M., Rollet A. P., Mathematical Models, Oxford, 1954 | MR

[46] Falckenberg H., “Anwendung der Dreiflachstheorie von E. Study auf reguläre Körper und verallgemeinerte konvexe Polyeder”, Mh. Math. Phys., 44 (1936), 285–289 | MR | Zbl

[47] Preudenthal H., v. d. Warden B. L., “Über eine Behauptung von Euklid”, Simon Stevin wis natuurk. Tijdschr., 25 (1947), 115–121

[48] Galafassi V. E., “I poliedri convessi con facce regolari equali”, Archimede, 12:4 (1960), 169–177 | MR | Zbl

[49] Grünbaum B., “On polyhedra in $E^3$ having all faces congruent”, Bull. Res. Council Israel, 8:4 (1960), 215–218 | MR

[50] Grünbaum V., Johnson N. W., “The faces of a regularfaced polyhedron”, J. London Math. Soc., 40:4 (1965), 577–586 | DOI | MR | Zbl

[51] Heppes A., “Isogonale spärische Hetse”, Ann. Univ. scient. Budapest, Sec. math., 7 (1964), 41–48 | MR | Zbl

[52] Hope S., “The nets of the regular star-faced and star pointed polyhedra”, Math. Gaz., 1951 35, 8–11 | DOI | MR | Zbl

[53] Jensen H., “The six Infinite regular polyhedra”, Math. Tidsskr., 1950, 53–60 | MR | Zbl

[54] Johnson N. W., “Convex polyhedra with regular faces”, abstract 576-157, Mimeographed notes (Carleton College, January 1961), Notices Amer. Math. Soc., 7, 1960, 952

[55] Johnson N. W., “Conrex polyhedra with regular faces”, Canad. J. Math., 18:1 (1966), 169–200 | MR | Zbl

[56] Kashikar P. K., “The Archimediam solids”, Math. Student, 2 (1934), 60–65 | Zbl

[57] Kibble W. F., “Regular polytopes inscribed in other regular polytopes”, Math. Student, 17 (1950), 26–31 | MR | Zbl

[58] v. Kol J. W. A., “On regular polyhedra and a theorem of Cauchy on convex polyhedra”, Niew Tijdschr. Wiskunde, 36 (1949), 237–244 | MR

[59] Kowalewski G., Der Eaplersche Körper und andere Banspiele, Leipzig, 1938

[60] Lesavre J., Mercier R., “Dix nouveaux polyedres semi-reguliers, sams plan de symetrie”, C. r. Acad. Sci., 224 (1947), 785–786 | MR | Zbl

[61] Lietzmann W., Anschauliche Einführung in die mehrdimensionale Geometrie, Müchen, 1952 | MR | Zbl

[62] Locher-Ernst L., “Wie viele regelmässige Bolyeder gibt es?”, Arch. Math., 3 (1952), 193–197 | DOI | MR | Zbl

[63] Matschinski M., “Decahexaedre regulier et une propriete speciale des espaces au nombre de dimensions egal a quatre ou superieur”, C. r. Acad. sci., 243:5 (1956), 472–475 | MR | Zbl

[64] Poinsot M., “Mémoire sur les Polygone et les Polyèdres”, J. de l'Ecole polytechn., 4 (1810), 16–48

[65] Rademacher H., “On the number of certain types of polyhadra”, Ill. J. Math., 9:3 (1965), 361–380 | MR | Zbl

[66] Robinson G. B., “On the fundamental region of a group, and the family of configurations wich arise therefrom”, J. Lond. math. Soc., 6 (1931), 70–75 | DOI | Zbl

[67] Roeser E., “Über die regulären hyperbolischen Polyeder mit unendlich vielen Flächen”, Jahresber. Deutsch. Math. Vereining., 43 (1933), 78–81 | Zbl

[68] Rossat H., “Uh noureau polyedre convexe semi-regulier”, Comp. r. “89 Contr. nat. Soc. savant Lion 1964”, 1 (1965), 39–50

[69] Sáenz G. C., “El arqimediano No 14”, Rev. Real. acad. cienc. exact., fis. y natur. Madrid, 59:2 (1965), 159–171

[70] Schläfli L., Gesam. math. Abhandl., b. I, Basel, 1950

[71] Shephard G. C., “Regular complex polytopes”, Proc. Lond. math. soc., 2 (1952), 82–97 | DOI | MR | Zbl

[72] Sommerville D. M. Y., “Isohedral and isogonal generalizations of the regular polyhedra”, Proc. Roy. Soc. Edinburgh, 52 (1932), 251–263 | Zbl

[73] Surrer F., “Über halbregulare Vielzelle im vierdimensionalen Raum”, Munchen, Diss., 1931, 1–75

[74] Toth L. F., Regulare Figuren, Leipsig, 1965

[75] Unkelbach H., “Die kantensymmetrischen, gleichkantigen Polyeder”, Deutsche Math., 1940, no. 4, 306–316 | MR | Zbl

[76] Grek A. S., “Pravilnye odnogranniki”, Uch. zap. Ivanovok, gos. ped. inst., 18 (1958), 179–200

[77] Grek A. S., “Pravilnye mnogogranniki prosteishikh giperbolicheskikh tipov”, Uch. zap. Ivanovsk. gos. ped. in-t, 34 (1963), 27–30 | MR

[78] Grek A. S., “Pravilnye mnogogranniki na poverkhnostyakh s eilerovoi kharakteristikoi $\chi=-4$”, Soobsch. AN GruzSSR, 42:1 (1966), 11–15

[79] Efremovich V. A., “Pravilnye mnogogranniki”, DAN SSSR, 57:3 (1947), 223–226 | MR

[80] Zamorzaev A. M., “O pravilnykh mnogostoronnikakh i mnogogrannikakh v prostranstve Lobachevskogo”, Uch. zap. Kishinevsk. un-t, 39 (1959), 195–207

[81] Lyubchenko V. M., “Ob odnom tipe mnogogrannikov”, Uch. zap. Kabard.-Balkarsk. un-t. Ser. fiz.-matem. N., 19 (1963), 193–194

[82] Polak V., “Odna problema, kasayuschayasya vypuklykh mnogogrannikov”, Časop. pěstov. mat., 87:2 (1962), 169–179 | Zbl

[83] Coxeter H. S. M., “Closepacking and froth”, Illinois J. Math., 1958, no. 4 BB, 746–758 | MR

[84] Degoli L., “Un notevole poliedro stellato”, Archimed, 13:1 (1961), 47–48 | MR

[85] Hawking A. F., Hill A. C., Reeve J. E., Tyrrell J. A., “On certain polyhedra”, Math. Gaz., 50:372 (1966), 140–144 | DOI

[86] Matschinski M., “Polytopes réguliers des séries du cube (PC) et du décahexaédre (PD)”, C. r. Acad. sci., 244:6 (1957), 717–720 | MR | Zbl