论文标题
替换为$ 2N $折的旋转对称性的离散平面瓷砖奇数n
Substitution discrete plane tilings with $2n$-fold rotational symmetry for odd n
论文作者
论文摘要
我们研究了也是离散平面瓷砖的替代瓷砖，即满足剪切和预测的放松版本。我们证明，带有2n倍旋转对称性的sub rosa取代，用于奇数n的旋转对称性大于5，而卡里和瑞萨南（Kari）和瑞萨南（Rissanen）定义的5个不是离散的平面，因此也不是切割和项目的瓷砖。然后，我们为任何奇数N定义了具有2倍旋转对称性的新平面Rosa取代砖，并表明这些旋转对称性满足离散平面条件。我们认为的瓷砖是边缘到边缘的菱形砖。我们为10倍的情况提供了明确的结构，并为任何奇数n的总体情况提供了一种构造方法。
We study substitution tilings that are also discrete plane tilings, that is, satisfy a relaxed version of cut-and-projection. We prove that the Sub Rosa substitution tilings with a 2n-fold rotational symmetry for odd n greater than 5 defined by Kari and Rissanen are not discrete planes, and therefore not cut-and-project tilings either. We then define new Planar Rosa substitution tilings with a 2n-fold rotational symmetry for any odd n, and show that these satisfy the discrete plane condition. The tilings we consider are edge-to-edge rhombus tilings. We give an explicit construction for the 10-fold case, and provide a construction method for the general case of any odd n.
