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space diagonal : ウィキペディア英語版
space diagonal

In geometry a space diagonal (or interior diagonal or body diagonal) of a polyhedron is a line connecting two vertices that are not on the same face. Space diagonals contrast with face diagonals, which connect vertices on the same face (but not on the same edge) as each other.〔William F. Kern, James R Bland,''Solid Mensuration with proofs'', 1938, p.116〕
== Axial diagonal==
An axial diagonal is a space diagonal that passes through the center of a polyhedron.
For example, in a cube with edge length ''a'', all four space diagonals are axial diagonals, of common length a\sqrt . More generally, a cuboid with edge lengths ''a'', ''b'', and ''c'' has all four space diagonals axial, with common length \sqrt.
A regular octahedron has 3 axial diagonals, of length a\sqrt , with edge length ''a''.
A regular icosahedron has 6 axial diagonals of length a\sqrt , where ''φ'' is the golden ratio (1+\sqrt 5)/2.〔.〕

抄文引用元・出典: フリー百科事典『 ウィキペディア(Wikipedia)
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