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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 114.8° and one angle of 80.75°. The pentagon has three short edges of unit length each, and two long edges of length . The acute angle is between the two long edges. If its dual snub cube has unit edge length, its surface area is and its volume is .
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