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Plotting Polyhedra

pchin 1371 Maple
July 05 2007
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Well, that last blog entry sure generated a lot of discussion! I'm going to move on to something a bit more fun and less controversial: how to generate a 3-D plot of a polyhedron. There are different ways to do this in Maple, depending on how complicated the polyhedron is and what else you want to do with it. I've uploaded a worksheet with a few simple examples. View 86_PolyhedraExample.mw on MapleNet or Download 86_PolyhedraExample.mw
View file details The easiest method is to use the plots[polyhedraplot] command. You can specify vertices of a polyhedron, or give a centre point and the option polytype=p, where p is the name of a polyhedron that Maple recognizes. To get the list of polyhedra, enter plots[polyhedra_supported](). The example worksheet shows my favourite polyhedron, the echidnahedron. (We have a stuffed echidna at home -- a gift to my kids from Australian friends.) Not all polyhedra that Maple can generate are available through polyhedraplot, but there are a good many. Another method is to use the plottools package to generate 2-d or 3-d objects like ellipses and octahedra. You can use other plottools commands to further transform these objects. For example, the stellate command can be used to get a stellation of a polyhedron. Note that this command creates a structure that must be passed to the plots[display] command. If you want to do computations with the polyhedra, you can create them with commands from the geom3d package. The geom3d[draw] command can then be used to display the objects. Canada is currently hosting the FIFA U-20 World Cup, so I added a Maple soccer ball to the example worksheet to show how one can combine geom3d and plot commands.
example display package

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