内容概述
如果一个多面体的所有面都是全等的正多边形，并且所有多面角也全等，它就是正多面体。虽然正多边形有无限多种，却只有五种正多面体：正四面体、立方体（正六面体）、正八面体、正十二面体、正二十面体。欧几里得《原本》第十三卷最早对它们作了系统处理；关于其名称由来的一个注释认为，正四面体、立方体、正十二面体应归功于毕达哥拉斯学派，而正八面体、正二十面体则归功于泰阿泰德。
中文正文
如果一个多面体的所有面都是全等的正多边形，所有多面角也全等，我们就说它是正多面体。奇怪的是，有无限多种正多边形，却只有 5 种正多面体。正多面体根据面的数目来命名，也就是，4 个正三角形的正四面体，6 个正方形的正六面体（立方体），8 个正三角形的正八面体，12 个正五边形的正十二面体，20 个正三角形的正二十面体（图 7）。
这些正多面体的早期历史已经湮没在遥远的过去之中。对它们的数学处理最早出现在欧几里得《原本》第十三卷里。该卷的第一个注释（完全可能是后来补充的，也许来自格米努斯（Geminus））指出，本卷“将处理所谓的柏拉图体，那名称实在是错了。因为其中的 3 种，正 4 面体、立方体和正 12 面体来自毕达哥拉斯学派，而正 8 面体和正 20 面体来自泰阿泰德（Theaetetus）。”事实也许真是这样。
英文正文
A polyhedron is said to be regular if its faces are congruent regular polygons and its polyhedral angles are all congruent. While there are regular polygons of all orders, it is surprising that there are only five different regular polyhedra. The regular polyhedra are named according to the number of faces each possesses. Thus there is the tetrahedron with 4 triangular faces, the hexahedron (or cube) with 6 square faces, the octahedron with 8 triangular faces, the dodecahedron with 12 pentagonal faces, and the icosahedron with 20 triangular faces. See Figure 7.
The early history of these regular polyhedra is lost in the dimness of the past. A mathematical treatment of them is initiated in Book XIII of Euclid's Elements. The first scholium (in all likelihood added later and probably taken from Geminus) of this book remarks that the book "will treat of the so-called Platonic solids, incorrectly named, because three of them, the tetrahedron, cube, and dodecahedron are due to the Pythagoreans, while the octahedron and icosahedron are due to Theaetetus." This could well be the case.
英语学习拓展
常用词汇
polyhedron音标/pɒliˈhiːdrən/
多面体。
原文用法：A polyhedron is said to be regular if its faces are congruent regular polygons...
regular音标/ˈreɡjʊlə/
正的；规则的。
原文用法：regular polygons / regular polyhedra
congruent音标/ˈkɒŋɡrʊənt/
全等的。
原文用法：its faces are congruent regular polygons
tetrahedron音标/ˌtetrəˈhiːdrən/
四面体。
原文用法：the tetrahedron with 4 triangular faces
hexahedron音标/ˌheksəˈhiːdrən/
六面体。
原文用法：the hexahedron (or cube) with 6 square faces
octahedron音标/ˌɒktəˈhiːdrən/
八面体。
原文用法：the octahedron with 8 triangular faces
dodecahedron音标/ˌdəʊdekəˈhiːdrən/
十二面体。
原文用法：the dodecahedron with 12 pentagonal faces
icosahedron音标/ˌaɪkɒsəˈhiːdrən/
二十面体。
原文用法：the icosahedron with 20 triangular faces
同义词与近义词
对应核心词汇：hexahedron
对应核心词汇：hexahedron。
辨析：cube 是日常用语，hexahedron 是强调“六面体”的几何术语。
常用短语与固定搭配
- regular polyhedron：正多面体。原文用法：there are only five different regular polyhedra。
- according to：根据。原文用法：named according to the number of faces。
- in all likelihood：十有八九。原文用法：The first scholium (in all likelihood added later...)
常用句式
- A is said to be B if ...：如果……，则称 A 为 B。原文例句：A polyhedron is said to be regular if its faces are congruent regular polygons and its polyhedral angles are all congruent.
长难句解析
A polyhedron is said to be regular if its faces are congruent regular polygons and its polyhedral angles are all congruent.
- 主干：A polyhedron is said to be regular。
- 修饰与从句：if 引导条件状语从句，从句中 its faces are congruent regular polygons 与 its polyhedral angles are all congruent 并列。
- 逻辑关系：条件满足时，多面体被称为“正的”。
语言使用特点
- 数学定义句常使用被动语态 is said to be，以保持客观性。
迁移练习
- 用英文写出五种正多面体的名称及对应面数。
- 用 A ... is said to be ... if ... 结构定义“正方形”。
点击展开参考答案
- tetrahedron (4), hexahedron/cube (6), octahedron (8), dodecahedron (12), icosahedron (20)。
- 示例：A quadrilateral is said to be a square if its four sides are equal and all its angles are right angles.