An unshellable triangulation of a tetrahedron
نویسندگان
چکیده
منابع مشابه
On Primitive Subdivisions of an Elementary Tetrahedron
A polytope P of 3-space, which meets a given lattice L only in its vertices, is called L-elementary. An L-elementary tetrahedron has volume ≥ (1/6). det(L), in case equality holds it is called L-primitive. A result of Knudsen, Mumford and Waterman, tells us that any convex polytope P admits a linear simplicial subdivision into tetrahedra which are primitive with respect to the bigger lattice (1...
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No acute tetrahedron is an 8-reptile
An r-gentiling is a dissection of a shape into r ≥ 2 parts which are all similar to the original shape. An r-reptiling is an r-gentiling of which all parts are mutually congruent. This article shows that no acute tetrahedron is an r-gentile or r-reptile for any r < 9, by showing that no acute spherical diangle can be dissected into less than nine acute spherical triangles.
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ژورنال
عنوان ژورنال: Bulletin of the American Mathematical Society
سال: 1958
ISSN: 0002-9904
DOI: 10.1090/s0002-9904-1958-10168-8