卵形體探究
Oloids & Faceted Oloids Experimentation
藏于芝加哥艺术学院视觉传达设计系
Collected in the Department of Visual Communication Design,
School of the Art Institute of Chicago
达雷尔-朗尼 · 坎福德纸 #炮铜色
2017年春;美国芝加哥
Daler-Rowney Canford paper #gun metal
spring 2017; Chicago, IL, USA
卵形体(音译:奥洛德体)是一种三维曲面几何体,由保罗・沙茨于1929年发现。其两端的凸曲线形由两个大小相同、相互垂直、彼此穿插的圆形构成,每个圆的圆心均落在另一个圆的圆周上。其曲面经运算可被切割为 6、12、40个等分切面,并由此衍生出无穷大的可能性。
An oloid is a three-dimensional curved geometric object that was discovered by Paul Schatz in 1929. It is the convex hull of a skeletal frame made by placing two linked congruent circles in perpendicular planes, so that the center of each circle lies on the edge of the other circle. Its curved surface can be mathematically divided into 6, 12, and 40 facets, which leads to unlimited possibilities.
萬花環探究
Kaleidocycle Experimentation
藏于芝加哥艺术学院视觉传达设计系
Collected in the Department of Visual Communication Design,
School of the Art Institute of Chicago
达雷尔-朗尼 · 坎福德纸 #卫兵红
2017年秋;美国芝加哥
Daler-Rowney Canford paper #guardsman red
fall 2017; Chicago, IL, USA
万花环是一种形体可变的柔性多面体。它将六个等腰四面体以对边相连的方式构成环形,可连续向内或向外翻转。除六边结构外,更高偶数边甚至非对称等腰四面体均可构成万花环。但与六边结构不同的是,不同的三角面比例会在万花环中心形成不同大小的空隙。
A kaleidocycle is a flexible polyhedron connecting six disphenoids on opposite edges into a cycle, which can be continuous twisted introversively or extroversively. Beyond 6 sides, higher even number of disphenoids or even assymetrical disphenoids can be chained together. These models will leave a central gap, depending on the proportions of the triangle faces.
對偶正多面體
Dual of Platonic Solids
藏于芝加哥艺术学院视觉传达设计系
Collected in the Department of Visual Communication Design,
School of the Art Institute of Chicago
达雷尔-朗尼 · 坎福德纸 #炮铜色、加拿大海报卡纸
2017年秋;美国芝加哥
Daler-Rowney Canford paper #gun metal, Canadian poster cardstock
spring 2017; Chicago, IL, USA
由古希腊哲学家柏拉图提出猜想的正多面体是三维欧几里得空间中的规则凸多面体,有且仅有正四面体、正方体、正八面体、正十二面体与正二十面体5个。若将其以特定几何关系剖开,即可得到另一个与之嵌套共生的对偶正多面体。
A Platonic solid—named after ancient Greek philosopher Plato—is a convex, regular polyhedron in three-dimensional Euclidean space. There are only five such polyhedra: tetrahedron, cube, octahedron, dodecahedron, and icosahedron.It can be cut apart into sections to reveal its corresponding dual, wihch is another enclosing symbiotic Platonic solid.
特别答谢余嘉悦、刘琉
Special Thanks to Yu, Jiayue & LIU, Liu