{"id":1072,"date":"2013-10-17T22:53:36","date_gmt":"2013-10-18T06:53:36","guid":{"rendered":"http:\/\/theiff.org\/current\/?p=1072"},"modified":"2013-10-17T22:54:33","modified_gmt":"2013-10-18T06:54:33","slug":"homochiral-tetrahedra-like-to-make-balls","status":"publish","type":"post","link":"https:\/\/theiff.org\/current\/liberation-geometry\/homochiral-tetrahedra-like-to-make-balls\/","title":{"rendered":"Homochiral Tetrahedra Like to Make Balls!"},"content":{"rendered":"

\"Jake<\/a><\/p>\n

 <\/p>\n

That’s the big news from my first week in residence at the IFF (Well, the first big news, anyway). \u00a0Maybe not necessarily surprising, but still pretty exciting nonetheless!<\/p>\n

I’ve been working with twisted tetrahedra in 3-D arrays for some time now, but always in arrangements that alternate between left-handed and right-handed orientations. \u00a0I call those hetero- (different) -chiral (handed) arrays and I’ve been really, really into them. \u00a0They make pretty straight lines in twelve different directions, and when I fit them together they feel fulfilled. \u00a0(Seriously, I don’t even think I’m projecting here, as I can say clearly and distinctly, that I also feel fulfilled) \u00a0And, heterochiral arrays of tetrahedra make a space filler (infinite 3d tiling of space): tetrahedra and truncated tetrahedra. So, there’s that as well (which is basically infinity). \u00a0But, I was never really interested in working with homo- (same) -chiral (handed) tetrahedral arrays until last week when I started making shapes here in the IFF Space. \u00a0I guess I was saving it for something special. \u00a0It turns out that homochiral tetrahedra are absolutely amazing when they are joined! \u00a0You just have to give them the space and support to do their own thing, which turns out to be: curve! \u00a0How about that!<\/p>\n

So, now I’ve got a partially stellated icosadodecahedron (20 triangles\/tetrahedra and 12 pentagons; pictured on the left, in blue and yellow), as well as a partially stellated truncated pentakisdodecahedron (At least, I think that’s what it is . . . 60 triangles\/tetrahedra, 12 pentagons, and 20 hexagons; on the right in black and white) But wait! There’s more! The partially stellated icosadodecahedral array is also a space filler, as the stellations are in fact tetrahedra on the faces of a regular icosadodecahedron. \u00a0Boom! Again with the infinity! I have a sneaking suspicion that the\u00a0partially stellated truncated pentakisdodecahedron has space filling potential too, but we’ll just have to see about that.<\/p>\n

I’m so looking forward to sharing all this, and more, at the space filling workshop we’re having this weekend! It’s such an exciting time to be with tetrahedra.<\/p>\n

I’m so happy to be here.<\/p>\n

-Jake Dotson<\/p>\n

 <\/p>\n

 <\/p>\n","protected":false},"excerpt":{"rendered":"

  That’s the big news from my first week in residence at the IFF (Well, the first big news, anyway). \u00a0Maybe not necessarily surprising, but still pretty exciting nonetheless! I’ve been working with twisted tetrahedra in 3-D arrays for some time now, but always in arrangements that alternate between left-handed and right-handed orientations. \u00a0I call […]<\/p>\n","protected":false},"author":2,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"_acf_changed":false,"footnotes":""},"categories":[6],"tags":[],"class_list":["post-1072","post","type-post","status-publish","format-standard","hentry","category-liberation-geometry"],"acf":[],"_links":{"self":[{"href":"https:\/\/theiff.org\/current\/wp-json\/wp\/v2\/posts\/1072","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/theiff.org\/current\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/theiff.org\/current\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/theiff.org\/current\/wp-json\/wp\/v2\/users\/2"}],"replies":[{"embeddable":true,"href":"https:\/\/theiff.org\/current\/wp-json\/wp\/v2\/comments?post=1072"}],"version-history":[{"count":10,"href":"https:\/\/theiff.org\/current\/wp-json\/wp\/v2\/posts\/1072\/revisions"}],"predecessor-version":[{"id":1083,"href":"https:\/\/theiff.org\/current\/wp-json\/wp\/v2\/posts\/1072\/revisions\/1083"}],"wp:attachment":[{"href":"https:\/\/theiff.org\/current\/wp-json\/wp\/v2\/media?parent=1072"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/theiff.org\/current\/wp-json\/wp\/v2\/categories?post=1072"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/theiff.org\/current\/wp-json\/wp\/v2\/tags?post=1072"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}