{"id":17706,"date":"2016-08-13T21:47:35","date_gmt":"2016-08-14T02:47:35","guid":{"rendered":"http:\/\/blog.kenperlin.com\/?p=17706"},"modified":"2016-08-13T21:47:35","modified_gmt":"2016-08-14T02:47:35","slug":"2x2x2x2-part-2","status":"publish","type":"post","link":"http:\/\/blog.kenperlin.com\/?p=17706","title":{"rendered":"2x2x2x2, part 2"},"content":{"rendered":"<p>If you look at the puzzle piece I showed yesterday within the Soma cube (<a href=https:\/\/en.wikipedia.org\/wiki\/Soma_cube>the Soma cube was invented by Piet Hein in 1936<\/a>), you can see that it takes up 4 out of the 27 positions in the assembled 3x3x3 cube:<\/p>\n<p><center><img decoding=\"async\" src=\"http:\/\/blog.kenperlin.com\/wp-content\/uploads\/2016\/08\/soma3d.jpg\" alt=\"soma3d\" width=300><\/center><\/p>\n<p>I am showing each of the component cubes as transparent blue, except for those inside the puzzle piece, which I am showing as transparent white.  You can see that the puzzle piece traces a path first right, then back, then down.<\/p>\n<p>Showing the parts of a 4D hypercube puzzle is a little trickier.  I don&#8217;t just want to show an exploded view, because I&#8217;d like the player to be able to see the puzzle as though it were a physical object, and rotate it interactively.<\/p>\n<p>So in addition to left\/right, down\/up, and back\/forward, I am adding the additional dimension of in\/out.  You can think of it as a kind of extra perspective dimension, as though things look smaller as they retreat away from us into this fourth dimension.<\/p>\n<p>Looked at this way, here is a puzzle piece within the 4D hypercube puzzle.  You can see that it takes up 5 out of the 16 positions in the assembled 4x4x4x4 hypercube:<\/p>\n<p><center><img decoding=\"async\" src=\"http:\/\/blog.kenperlin.com\/wp-content\/uploads\/2016\/08\/soma4d.jpg\" width=300><\/center><\/p>\n<p>Again, I am showing each of the component hypercubes as transparent blue, except for those inside the puzzle piece, which I am showing as transparent white.  You can see that the puzzle piece traces a path first out, then right, then back, then down.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>If you look at the puzzle piece I showed yesterday within the Soma cube (the Soma cube was invented by Piet Hein in 1936), you can see that it takes up 4 out of the 27 positions in the assembled 3x3x3 cube: I am showing each of the component cubes as transparent blue, except for &hellip; <a href=\"http:\/\/blog.kenperlin.com\/?p=17706\" class=\"more-link\">Continue reading<span class=\"screen-reader-text\"> &#8220;2x2x2x2, part 2&#8221;<\/span><\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":[],"categories":[1],"tags":[],"_links":{"self":[{"href":"http:\/\/blog.kenperlin.com\/index.php?rest_route=\/wp\/v2\/posts\/17706"}],"collection":[{"href":"http:\/\/blog.kenperlin.com\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"http:\/\/blog.kenperlin.com\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"http:\/\/blog.kenperlin.com\/index.php?rest_route=\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"http:\/\/blog.kenperlin.com\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=17706"}],"version-history":[{"count":2,"href":"http:\/\/blog.kenperlin.com\/index.php?rest_route=\/wp\/v2\/posts\/17706\/revisions"}],"predecessor-version":[{"id":17710,"href":"http:\/\/blog.kenperlin.com\/index.php?rest_route=\/wp\/v2\/posts\/17706\/revisions\/17710"}],"wp:attachment":[{"href":"http:\/\/blog.kenperlin.com\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=17706"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"http:\/\/blog.kenperlin.com\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=17706"},{"taxonomy":"post_tag","embeddable":true,"href":"http:\/\/blog.kenperlin.com\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=17706"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}