منابع مشابه
Regular Simplices Passing through Holes
What is the smallest circular or square wall hole that a regular tetrahedron can pass? This problem was solved by Itoh–Tanoue– Zamfirescu [8]. Then, we settled the case of equilateral triangular hole in [1]. Motivated by these results, we consider the corresponding problems in higher dimensions. Among other results, we determine the minimum (n−1)-dimensional ball hole that a unit regular n-simp...
متن کاملA Statistical Characterization of Regular Simplices
Picture three points at the vertices of an equilateral triangle in two dimensions, or four points at the vertices of a regular tetrahedron in three dimensions. Thought of as scatterings of data they wouldn’t seem to reveal strong linear associations between the coordinates. There are no clear axes of elongation in the scatterplots, which would suggest that change in some variable is predictable...
متن کاملLarge regular simplices contained in a hypercube
We prove that the n-dimensional unit hypercube contains an n-dimensional regular simplex of edge length c √ n, where c > 0 is a constant independent of n. Let l∆n be the n-dimensional regular simplex of edge length l, and let lQn be the n-dimensional hypercube of edge length l. For simplicity, we omit l if l= 1, e.g., Qn denotes the unit hypercube. We are interested in the maximum edge length o...
متن کاملIsosurfaces on Optimal Regular Samples
Volumetric samples on Cartesian lattices are less efficient than samples on body-centred cubic (BCC) lattices. We show how to construct isosurfaces on BCC lattices using several different algorithms. Since the mesh that arises from BCC lattices involves a large number of cells, we show two alternate methods of reducing the number of cells by clumping tetrahedra into either octahedra or hexahedr...
متن کاملContainment and Inscribed Simplices
Let K and L be compact convex sets in Rn. The following two statements are shown to be equivalent: (i) For every polytope Q ⊆ K having at most n+ 1 vertices, L contains a translate of Q. (ii) L contains a translate of K. Let 1 ≤ d ≤ n − 1. It is also shown that the following two statements are equivalent: (i) For every polytope Q ⊆ K having at most d+ 1 vertices, L contains a translate of Q. (i...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Discrete & Computational Geometry
سال: 1994
ISSN: 0179-5376,1432-0444
DOI: 10.1007/bf02574000