Editing Space diagonal (section)

== 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 <math>a\sqrt {3}.</math> More generally, a [[cuboid]] with edge lengths ''a'', ''b'', and ''c'' has all four space diagonals axial, with common length <math>\sqrt{a^2+b^2+c^2}. </math>

A regular [[octahedron]] has 3 axial diagonals, of length <math>a\sqrt {2}</math>, with edge length ''a''. 

A [[regular icosahedron]] has 6 axial diagonals of length <math>a\sqrt {2+\varphi}</math>, where <math>\varphi</math> is the [[golden ratio]] <math>(1+\sqrt 5)/2</math>.<ref>{{citation|title=Platonic & Archimedean Solids|series=Wooden Books|first=Daud|last=Sutton|publisher=Bloomsbury Publishing USA|year=2002|isbn=9780802713865|page=55|url=https://books.google.com/books?id=vgo7bTxDmIsC&pg=PA55}}.</ref>