tag:blogger.com,1999:blog-2417641727801397965.post1810225098764865815..comments2021-12-25T10:32:04.390-06:00Comments on roice: Soap BubblesRoice Nelsonhttp://www.blogger.com/profile/11303336118982649682noreply@blogger.comBlogger2125tag:blogger.com,1999:blog-2417641727801397965.post-55565351575411279232010-07-26T19:44:27.200-05:002010-07-26T19:44:27.200-05:00I see what you're getting at, though a polycho...I see what you're getting at, though a polychoron isn't accurately described as such. It seems fair to make a statement like this about the volume enclosed by this particular projection of this particular 4D object (though it would be the intersection of six spheres rather than four - this would be easier to see if I had an animation rotating the picture around). But the 8-cell lives in 4 dimensions, and is built up of 8 non-intersecting portions of the hypersphere. These 8 "cells" touch each other at boundaries that are portions of 2D spheres. There are 24 of these spherical boundaries, and they are the soap films rendered in the picture, though many of them look flat instead of spherical due to the projection. Other polychora will have different properties than the 8-cell.Roice Nelsonhttps://www.blogger.com/profile/11303336118982649682noreply@blogger.comtag:blogger.com,1999:blog-2417641727801397965.post-29356717189683222452010-07-23T14:10:23.279-05:002010-07-23T14:10:23.279-05:00is the Polychoron the intersection of 4 spheres?...is the Polychoron the intersection of 4 spheres?<br />mario<br />mariodegrossi@gmail.commario de grossihttp://www.wayofthetree.comnoreply@blogger.com