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具有七个顶点的多面体是稀少的。Polyhedra with seven vertices are rare.

每一个理想的多面体是依次由三角形组成。Each of these perfect polyhedra would be in turn composed of triangles.

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可靠性的获得是建立在多面体的三角面片表示基础之上。The robustness is achieved by triangle-based representations of polyhedra.

现在，在我们的理论中，我们把多面体的形象丢掉，留著图就好了。Now in our theory, we throw away the drawings of polyhedra and just keep the graphs.

提出的算法，用于计算两个凸多面体之间的最小距离。An algorithm for computing the minimum distance between two convex polyhedra is presented.

然后，提出了一种针对简单多面体模型的连续域中轴变换算法。After that, a new algorithm in continuous domain for Medial Axis Transform of polyhedra is presented.

尤其是，有些用奇怪方式连接的图，并不能转换成整齐的多面体图案。In particular, some graphs connect in strange ways that cannot be converted into a tidy picture of polyhedra.

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COLLIDE是一个交互式的和确切的冲突检验库，它用于由凸起的多面体组成的大的环境中。I_COLLIDE is an interactive and exact collision detection library for large environments composed of convex polyhedra.

我们建构的多面体，比较像是用牙签插在软糖上弄成的。The polyhedra we had built were rather like structures made of toothpicks stuck into blobs of marshmallow at the corners.

研究了晶体中负离子配位多面体的结晶方位与晶体结晶形貌之间的关系。The relations between the morphology and the orientations of the anion coordination polyhedra in the crystals are studied.

转换研究方向的另一个原因是，我们后来发现合成的柱条多面体并不够坚固。Another reason for changing direction was that along the way we realized that the stick polyhedra we had built were not rigid.

现在任教于美国普渡大学的毛成德与我利用类似柱条多面体的DNA平行四边形，成功合成了二维平面的图案。Chengde Mao, now at Purdue University, and I have made two-dimensional patterns from DNA parallelograms similar to our stick polyhedra.

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对多面体中轴点进行了分类，并揭示了不同类中轴点之间的几何关系。A classification of the Medial Axis points in polyhedra is introduced, and the correlative relation of these Medial Axis points is discussed.

本文讨论了晶体表面结构和负离子配位多面体结晶方位的关系。The relationship between the crystallographic orientation of anionic coordination polyhedra and the surface structures was discussed in this paper.

比如说，要是空间是弯曲的，不管我们用任何画法，都不能把一堆多面体适当地嵌合在一起，可是，我们还是很容易把图画出来。For example, whenever space is curved, the polyhedra will not fit together properly in any drawing we could do, yet we can still easily draw a graph.

本文讨论了配位多面体的群重叠积分计算问题，给出了这种群重叠积分的一般形式以及它们满足的一些关系。The formulation of group overlap integrals in coordination polyhedra is discussed. The basic expressions and some sum relations of group overlap integrals are given.

指出了晶体表面结构，显示了负离子配位多面体在晶体生长过程中的结晶轨迹。It is suggested that the surface structures show the locus formed by the combination of growth units of anionic coordination polyhedra on different surfaces during crystal growth.

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该算法面向动态复杂场景采用层次的自适应空间剖分方法建构物体的平衡包围盒树，然后通过并行遍历包围盒树来加速碰撞检测。The algorithm builds BoxTreees of arbitrary non convex polyhedra using a hierarchical adaptive space subdivision scheme, and speeds up collision detection by traversing the BoxTrees in parallel.

多角和对称的多面体显示为图的概括的，分子结构模型，如诺贝尔奖获奖富勒烯奖，化学和晶体发生。Polycycles and symmetric polyhedra appear as generalizations of graphs in the modeling of molecular structures, such as the Nobel prize winning fullerenes, occurring in chemistry and crystallography.