Abstract
We present a general geometric description and Euler-Poincaré characteristics of middle-sectioned simplices in a four-dimensional affine space. We demonstrate the relationship between similar geometric objects and four-dimensional analogs of the triangular Sierpinski napkin.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
M. Berger, Géométrie [Russian translation], Vol. 1, Mir, Moscow (1984).
H. S. M. Coxeter, Introduction to Geometry, Wiley, New York (1961).
L. A. Lyusternik, Convex Figures and Polyhedrons [in Russian], Gostekhteorizdat, Moscow (1956).
J. Feder, Fractals, Plenum, New York (1988).
A. D. Aleksandrov, Convex Polyhedrons [in Russian], Gostekhteorizdat, Moscow (1950).
M. V. Prats’ovytyi, Fractal Approach to the Investigation of Singular Distributions [in Ukrainian], National Pedagogic University, Kyiv (1998).
Yu. S. Reznikova, “Analytic-geometric description of the Sierpinski carpet and its three-dimensional analog in terms of Galitsyn modulus,” Nauk. Chasopys Drahomanov Nats. Ped. Univ., Ser. 1, Fiz.-Mat. Nauky, No. 5, 207–216 (2004).
Author information
Authors and Affiliations
Additional information
__________
Translated from Ukrains’kyi Matematychnyi Zhurnal, Vol. 59, No. 4, pp. 566–570, April, 2007.
Rights and permissions
About this article
Cite this article
Reznikova, Y.S. Middle-sectioned simplices in a four-dimensional affine space. Ukr Math J 59, 633–638 (2007). https://doi.org/10.1007/s11253-007-0042-z
Received:
Revised:
Issue Date:
DOI: https://doi.org/10.1007/s11253-007-0042-z