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<blockquote data-quote="TheCosmicKid" data-source="post: 7428297" data-attributes="member: 6683613"><p>The regular dodecahedron vexes me. Why do its faces have to be pentagons? What has five got to do with twelve? It's the one number less than six that <em>isn't</em> a factor of twelve! The <em>rhombic</em> dodecahedron is the d12 of a gentleperson, its bold geometry made up of pleasantly twelve-making fours and threes, just far enough outside the Platonic mainstream to be intriguing but not so far as to be vulgar. And for the truly avant-garde, there is the <em>secret</em> rhombic dodecahedron, the Bilinski dodecahedron, only discovered in the 1970s, with its lean and efficient golden-ratioed faces. If somebody shows up at your table with a Bilinski d12, you can be sure they are on the very cutting edge of science and engineering. Because they clearly have access to a 3D printer. Because I haven't seen Bilinskis on sale anywhere.</p></blockquote><p></p>
[QUOTE="TheCosmicKid, post: 7428297, member: 6683613"] The regular dodecahedron vexes me. Why do its faces have to be pentagons? What has five got to do with twelve? It's the one number less than six that [I]isn't[/I] a factor of twelve! The [I]rhombic[/I] dodecahedron is the d12 of a gentleperson, its bold geometry made up of pleasantly twelve-making fours and threes, just far enough outside the Platonic mainstream to be intriguing but not so far as to be vulgar. And for the truly avant-garde, there is the [i]secret[/I] rhombic dodecahedron, the Bilinski dodecahedron, only discovered in the 1970s, with its lean and efficient golden-ratioed faces. If somebody shows up at your table with a Bilinski d12, you can be sure they are on the very cutting edge of science and engineering. Because they clearly have access to a 3D printer. Because I haven't seen Bilinskis on sale anywhere. [/QUOTE]
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