Constructions of triangular and quadrangular polyhedra of inscribable type

Ernest Jucovič; Sergej Ševec; Marián Trenkler

Mathematica Slovaca (1997)

  • Volume: 47, Issue: 3, page 313-317
  • ISSN: 0232-0525

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Jucovič, Ernest, Ševec, Sergej, and Trenkler, Marián. "Constructions of triangular and quadrangular polyhedra of inscribable type." Mathematica Slovaca 47.3 (1997): 313-317. <http://eudml.org/doc/32404>.

@article{Jucovič1997,
author = {Jucovič, Ernest, Ševec, Sergej, Trenkler, Marián},
journal = {Mathematica Slovaca},
keywords = {polyhedron; inscribable type},
language = {eng},
number = {3},
pages = {313-317},
publisher = {Mathematical Institute of the Slovak Academy of Sciences},
title = {Constructions of triangular and quadrangular polyhedra of inscribable type},
url = {http://eudml.org/doc/32404},
volume = {47},
year = {1997},
}

TY - JOUR
AU - Jucovič, Ernest
AU - Ševec, Sergej
AU - Trenkler, Marián
TI - Constructions of triangular and quadrangular polyhedra of inscribable type
JO - Mathematica Slovaca
PY - 1997
PB - Mathematical Institute of the Slovak Academy of Sciences
VL - 47
IS - 3
SP - 313
EP - 317
LA - eng
KW - polyhedron; inscribable type
UR - http://eudml.org/doc/32404
ER -

References

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  1. DILLENCOURT M. B-SMITH W. D., A linear time algorithm for testing the inscribability of trivalent polyhedra, Internat. J. Comput. Geom. Appl. 5 (1995), 21-36. (1995) MR1331174
  2. DILLENCOURT M. B.-SMITH W. D., A simple method for resolving degeneracies in Delaunay triangulations, In: Automata, Languages, and Programming: Proc. 20th Internal. Coll., Lund Sweden ICALP, Lund, Sweden, July 1993. Lecture Notes in Comput. Sci. 700, Springer, Berlin-New York, 1993, pp. 177-188. (1993) MR1252411
  3. GRÜNBAUM B., On Steinitz's theorem about non-inscribable polyhedra, Nederl. Akad. Wetensch. Proc. Ser. A 66 (1963), 452-455. (1963) Zbl0115.15005MR0152945
  4. GRÜNBAUM B.-SHEPHARD G. C., Some problems on polyhedra, J. Geom. 29 (1987), 182-190. (1987) Zbl0618.52004MR0904573
  5. HARARY F., Graph Theory, Addison Wesley, Reading, 1969. (1969) Zbl0196.27202MR0256911
  6. HODGSON C. D.-RIVIN I.-SMITH W. D., A characterization of convex hyperbolic polyhedra and of convex polyhedra inscribed in the sphere, Bull. Amer. Math. Soc. (N.S.) 27 (1992), 246-251. (1992) Zbl0759.52010MR1149872
  7. JUCOVIČ E.-ŠEVEC S., Note on inscribability of quadrangular polyhedra with restricted number of edge-types, J. Geom. 42 (1991), 126-131. (1991) Zbl0742.52011MR1132841
  8. STEINER J., Systematische Entwicklung der Abhängigkeit geometrischer Gestalten von einander, Reimer, Berlin, 1832; Jacob Steiner's Collected Works, Vol. 1, Berlin, 1881. Zbl0015.36602
  9. STEINITZ E., Uber isoperimetrische Probleme bei konvexen Polyedern I; II, J. Reine Angew. Math. 158; 159 (1927; 1929), 129-153; 133-143. (1927) 

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