# 柏拉圖立體20點

1.為什麼只有正三角形才可以拼湊成3種不同的立體

2.足球是由哪個立體切出來的

3.為什麼只有這五種 才能為『正』的立體

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Update 2:

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Lv 7

1 and 3

(1) Each vertex of the solid must coincide with one vertex each of at least three faces.

(2) At each vertex of the solid, the total, among the adjacent faces, of the angles between their respective adjacent sides must be less than 360.

(3) The angles at all vertices of all faces of a Platonic solid are identical, so each vertex of each face must contribute less than 360/3=120.

(4) Regular polygons of six or more sides have only angles of 120 or more, so the common face must be the triangle, square, or pentagon. And for:

(5) Triangular faces: each vertex of a regular triangle is 60, so a shape may have 3, 4, or 5 triangles meeting at a vertex; these are the tetrahedron, octahedron, and icosahedron respectively.

(6) Square faces: each vertex of a square is 90, so there is only one arrangement possible with three faces at a vertex, the cube.

(7) Pentagonal faces: each vertex is 108; again, only one arrangement, of three faces at a vertex is possible, the dodecahedron.

2 足球是由dodecahedron切出來的

• 育賢
Lv 4