A dihedral acute triangulation of the cube
نویسندگان
چکیده
It is shown that there exists a dihedral acute triangulation of the three-dimensional cube. The method of constructing the acute triangulation is described, and symmetries of the triangulation are discussed.
منابع مشابه
Acute Triangulations of Polyhedra and R
We study the problem of acute triangulations of convex polyhedra and the space R. Here an acute triangulation is a triangulation into simplices whose dihedral angles are acute. We prove that acute triangulations of the n-cube do not exist for n≥4. Further, we prove that acute triangulations of the space R do not exist for n≥5. In the opposite direction, in R, we present a construction of an acu...
متن کاملAcute triangulations of polyhedra and ℝ N
We study the problem of acute triangulations of convex polyhedra and the space Rn. Here an acute triangulation is a triangulation into simplices whose dihedral angles are acute. We prove that acute triangulations of the n–cube do not exist for n ≥ 4. Further, we prove that acute triangulations of the space Rn do not exist for n ≥ 5. In the opposite direction, in R3, we present a construction of...
متن کاملTiling space and slabs with acute tetrahedra
We show it is possible to tile three-dimensional space using only tetrahedra with acute dihedral angles. We present several constructions to achieve this, including one in which all dihedral angles are less than 77.08◦, and another which tiles a slab in space. 1 Problem definition Triangulations of two and three-dimensional domains find numerious applications in scientific computing, computer g...
متن کاملTriangulation of Simple 3D Shapes with Well-Centered Tetrahedra
A completely well-centered tetrahedral mesh is a triangulation of a three dimensional domain in which every tetrahedron and every triangle contains its circumcenter in its interior. Such meshes have applications in scientific computing and other fields. We show how to triangulate simple domains using completely well-centered tetrahedra. The domains we consider here are space, infinite slab, inf...
متن کامل. C O ] 1 1 A pr 2 00 2 ASYMPTOTICALLY EFFICIENT TRIANGULATIONS OF THE d - CUBE
We describe a method to triangulate P × Q which is very useful to obtain triangulations of the d-cube I of good asymptotic efficiency. The main idea is to triangulate P × Q from a triangulation of Q and another of P ×∆, where ∆ is a simplex of dimension m− 1, which is supposed to be smaller than dim(Q) = n− 1. Last triangulation will induce a triangulation of P ×∆. Thus, considering P := I and ...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید
ثبت ناماگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید
ورودعنوان ژورنال:
- Comput. Geom.
دوره 43 شماره
صفحات -
تاریخ انتشار 2010