Alan Michelson <amichelson2002@...> wrote:You can get over a hundred of them Voronoi Cells -- in a four-dimensional hecatonicosachoron or 120-cell. But...
... Both: http://mathworld.wolfram.com/KeplerConjecture.html http://mathworld.wolfram.com/KelvinsConjecture.html ... There is a lot of talk about A-mod and...
I finally found out how duoprisms work in 4-space! You can combine any too regular polygons. My first animation is what I'm calling a pentagrammic duoprism,...
It doesn't look like you have the dispentachoron up yet. This is a fascinating 4-dimensional polytope that you can see -- and hear! -- in this spreadsheet (for...
We are an academic research group of National Kaohsiung First University of Science and Technology in TAIWAN. To do research of knowledge management in...
When you rotate a cube, each square gets in front of the other square. So you're seeing the farther square framed by the nearer square. It is similar with the...
Hi y'all this is perhaps a bit more of a mundane question.... for an art project i need to find an equation that allows me find the edge lengths of either...
Yes, geometry can be very weird. For example, in two-dimensional geometry, there can be an infinite number of regular convex polygons (All of which are...
The four-dimensional version of the regular icosahedron is the 600-cell. http://mathworld.wolfram.com/600-Cell.html The four-dimensional version of the regular...
The star tetrahedron is like unfolding the pentatope to fit on our familiar 3-space. In actuality, the tets are bonded to each other and wrap around in...
Inside-of-Outside or Outside-of-Inside? That's all confusing in 4-dimensional space. By the way, the Klein bottle is really a 4-dimensional manifold. The...
When the hypercube rotates, the cubes trade places. The "inside" cube becomes the "outside" cube, and vice versa! When the 24-cell rotates, the projection...
wow! thats the event i'm being sent to set up my art at- cool! i will even have a piece constructed using the ratios i was so grciously sent! ciao- andres ... ...
... Hey Andre, What given sphere radius? The insphere, midsphere, or circumsphere? I'm asuming you want the edges of this compound to be perpendicular...
I've got an animation of the Grand Antiprism! Well, four, really... One of the very beastie itself, and to help in visualization, one of a single ring of 10...
it depends on what is the temperature of the water. If it is liquid there is no stable structure, all molecules are moving and vibrating chaotically. Only when...
http://www.lsbu.ac.uk/water/index.html This is a link to Dr. Martin Chaplin's interesting research results. It seems that liquid water may be weakly clustered...
This reminds me of the ~90 degree superconductor model the was resolved by IBM researchers many years ago. Of course the superconducting made the model...
Each icosahedron has a volume of 20, but since each tet is shared by 4 icos, then there are 600 tets rather than 2400 tets. (120 icos of volume 20 equals 2400...
In 4-D hyperspace, each icosahedral cap (of the 600-cell) has a volume of 20 tets, just as each pentagonal cap (of the icosahedron) has an area of 5...
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