每个面都是凹多边形的多面体

昨晚做梦,梦见了一个有趣的数学问题:有没有什么多面体,它的每个面都是凹多边形?有趣的是,接下来我梦见自己醒了过来,然后立即上网寻找答案。我梦见我查到了相关的论文,论文作者的名字中出现了很多奇怪的符号。我梦见我开始研究论文作者的名字该怎么发音。我梦见我研究了半天没有进展,于是踏上了拜访作者本人的路……

然后就彻底醒了。然后立即上网寻找答案。废话不多说了。Branko Grünbaum 和 G. C. Shephard 在 1998 年的论文《Isohedra with Nonconvex Faces》中给出了一些例子。下图是我很喜欢的一个例子。整个多面体由12个全等的凹多边形组成。

15 条评论

  • empty

    更新了!!!

  • localhost

    已阅。

  • chirsz

    新年快乐 M 大!

  • Han

    新年快乐哈

  • Twailait_Sparkle

    前排祝Matrix67前辈新年快乐!该十二面体可构造如下:标出立方体各棱中点并连接,使1)每个正方形面均有唯一线段将其二等分,2)互相平行的面上线段平行,互相垂直的面上线段异面垂直;然后保持原立方体顶点不动,将连接所成六条线段同等地缩短并向面内凹陷。如果把线段同等地拉长并向面外突出,则得一种叫pyritohedron的凸多面体,其得名于黄铁矿pyrite的常见晶体外形,每个镜面对称的五边形面有四边等长和另一边与之不等(若相等则成正十二面体)。上述两个十二面体均有T_h的对称性,具体可查维基百科pyritohedral symmetry。最后,把这个pyritohedron磨圆了可以当排球打🏐

  • smite

    有意思

  • zemora

    这就没了?

  • 有趣
    ps,居然这么久还没有人评论… 看来文字博客类淡入人们的视线了

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  • jerictica1

    interesting

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