I am trying to draw a tetrahedron and square based pyramid, having its triangular faces the same asthat of the tetrahedron. While the geom3d package in Maple 7 has several polyhedra, a pyramid, or pentahedron(?) seem to be missing. The closest is the octohedron - but this is two square pyramids "glued" together! I'm totally bamboozled by the Polyhedron command with all its options. Is it possible to somehow cut the octohedron in two, to get a pyramid? Below is my Maple program, including at the end aplottools command to draw a separate ocotohedron.
Any help gratefully received.
> #Puzzle Problem with tetrahedron and pyramid. How many faces will
> #resultant polyhedron have when a triangular face of the pyramid is "glued" to the tetrahedron.
> print(`A pyramid and tetrahedron are shown: the triangular faces of each being the same dimensions. The`);
> print(`triangular face of the pyramid is attached to a triangular face of the tetrahedron.`);
> print(`How many faces does the resulting polyhedron have?`);
> print(` a.) 5 b.) 6 c.) 7 d.) 8 e.) 9`);
> # octahedron, hexahedron, cube, icosahedron, dodecahedron - but pentahedron not supported in Maple 7 :-(
> draw([d(color=red),t(color=green)],title=`Tetrahedron & pyramid`,orientation=[45,45]);
> f := octahedron([0,0,0],1): #, octahedron([1,1,1],0.5):