“Platonic solid”的概念、定义、习题解题方法及翻译-数学辞典

单词

Platonic solid

释义

Platonic solid

A convex polyhedron is regular if all its faces are alike and all its vertices are alike. More precisely, this means that

(i) all the faces are regular polygons having the same number p of edges, and

(ii) the same number q of edges meet at each vertex.

Notice that the polyhedron shown here, with 6 triangular faces, satisfies (i) but is not regular because it does not satisfy (ii).

This solid is face-transitive but not regular

There are five regular convex polyhedra, known as the Platonic solids:

(i) the regular tetrahedron, with 4 triangular faces (p = 3, q = 3),

(ii) the cube, with 6 square faces (p = 4, q = 3),

(iii) the regular octahedron, with 8 triangular faces (p = 3, q = 4),

(iv) the regular dodecahedron, with 12 pentagonal faces (p = 5, q = 3),

(v) the regular icosahedron, with 20 triangular faces (p = 3, q = 5).

See also edge-transitive, face-transitive, Ludwig, Schläfli, Schläfli symbol, vertex-transitive.

随便看

数学辞典收录了4151条数学词条，基本涵盖了常用数学知识及数学英语单词词组的翻译及用法，是数学学习的有利工具。