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- W4298081815 abstract "Let P be a finite set of points in the 3-dimensional Euclidean space ℝ3 in general position. For x0,x1,x2,x3∈P, let H+(x0;x1,x2,x3) (resp. res.H−(x0;x1,x2,x3)) denote the open half space containing x0 (resp. not containing x0) and bounded by the plane containing x1,x2,x3. Further let P(x0;x1,x2,x3):=P∩H+(x1;x0,x2,x3)∩H+(x2;x0,x1,x3)∩H+(x3;x0,x1,x3). In this paper, we show the following statement: if | P |≥4, and if κ1,κ2,κ3,κ4 are integers with κ1+κ2+κ3+κ4=| P |−4,0≤κ1,κ2,κ3,κ4≤| P |−22 and κ1+κ2≤| P |−22, then for any p1,p2∈P(p1≠p2), there exist q1,q2∈P such that the convex hull of { p1,p2,q1,q2 } is a 3-simplex (tetrahedron) containing no point of P in its interior and such that |P(p1;p2,q1,q2)≤k1≤P∩H−(p1;p2,q1,q2)|,|P(p2;p1,q1,q2)≤k2≤P∩H−(p2;p1,q1,q2)|,|P(q1;q2,p1,p2)≤k3≤P∩H−(q1;q2,p1,p2)|,|P(q2;q1,p1,p2)≤k4≤P∩H−(q2;q1,p1,p2)|." @default.
- W4298081815 created "2022-10-01" @default.
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- W4298081815 date "1995-06-01" @default.
- W4298081815 modified "2023-10-07" @default.
- W4298081815 title "A CELLULAR SIMPLEX WITH PRESCRIBED NUMBERS OF POINTS IN REGIONS DETERMINED BY ITS FACETS" @default.
- W4298081815 doi "https://doi.org/10.55937/sut/1262208448" @default.
- W4298081815 hasPublicationYear "1995" @default.
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