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pentagonal icositetrahedron : ウィキペディア英語版
pentagonal icositetrahedron

In geometry, a pentagonal icositetrahedron or pentagonal icosikaitetrahedron〔Conway, Symmetries of things, p.284〕 is a Catalan solid which is the dual of the snub cube. In crystallography it is also called a gyroid.〔http://www.metafysica.nl/turing/promorph_crystals.html〕〔http://www.tulane.edu/~sanelson/eens211/forms_zones_habit.htm〕
It has two distinct forms, which are mirror images (or "enantiomorphs") of each other.
== Geometry==
Denote the tribonacci constant by ''t'', approximately 1.8393. (See snub cube for a geometric explanation of the tribonacci constant.) Then the pentagonal faces have four angles of \cos^\left(\frac\right)\approx 114.8° and one angle of \cos^(2-t)\approx 80.75°. The pentagon has three short edges of unit length each, and two long edges of length \frac\approx1.42. The acute angle is between the two long edges.
If its dual snub cube has unit edge length, its surface area is \scriptstyle\sqrt} \scriptstyle and its volume is \sqrt} \scriptstyle.

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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