墙纸群是什么？一共多少种？
What is a wallpaper group, and how many are there?
墙纸群是平面上所有能无缝平铺的对称群（平移、旋转、反射、滑移反射），共17种。它们把‘重复的平面图案’做了完整分类。
Wallpaper groups are the symmetry groups (translations, rotations, reflections, glide reflections) of repeating plane tilings; there are exactly 17. They fully classify periodic plane patterns.
难度 专业 · 适合 大众
CC BY 4.0 · 已核验 · Verified 2026-08-23 · 2 条独立证据
来源 · Source
Courant & Robbins,《What Is Mathematics?》Oxford University Press,1996 第二版;中译《什么是数学》
R. Courant and H. Robbins, What Is Mathematics?, Oxford University Press, 1996; Chinese ed.
独立核验依据 · Independent verification: 核验依据 2 OPENLIBRARY 标识 /works/OL811195W：What is mathematics?（按标题
#对称群 #分类
晶体里的对称为什么最多只有 230 种空间群？
Why are there at most 230 space groups of crystal symmetries?
三维空间中平移加点对称（旋转、反射、螺旋、滑移）的组合方式被数学完全分类，恰好230种。它解释了为什么自然界晶体外观虽多、对称类型却有限。
In 3D, all combinations of translations with point symmetries (rotation, reflection, screw, glide) are fully classified into exactly 230 space groups. It explains why crystals vary in look but not in symmetry types.
难度 专业 · 适合 大众
CC BY 4.0 · 已核验 · Verified 2026-08-23 · 2 条独立证据
来源 · Source
Courant & Robbins,《What Is Mathematics?》Oxford University Press,1996 第二版;中译《什么是数学》
R. Courant and H. Robbins, What Is Mathematics?, Oxford University Press, 1996; Chinese ed.
独立核验依据 · Independent verification: 核验依据 2 OPENLIBRARY 标识 /works/OL811195W：What is mathematics?（按标题
#对称群 #晶体