create a collection of vertex for a solid with a collection of Planes?
I want to draw mineral crystal with Geogebra. Basically, I input a collection of Planes in 3D, and want to get the solid which is enclosed with all these Planes.
Take octahedron for example, i cannot use the octahedron command, since crystal in real world does not have the theoretical shape, it is just all eight surface keep the same angle as octahedron, but different surface can have different distance to the center point of the crystal.
A Plane is represented with equation: ax+by+cz=k. So, I define two lists for my "octahedron":
one list named "O" is for the eight "k"s of the equations, which is proportional to the distance of the plane to point (0,0,0).
the other list named "Oabc" is a matrix of the eight a,b,c coefficient, which represents intercepts on three axis.
Then, i can define a sequence of eight Planes named "OPlanes" with these two lists.
Next, i get sequence named "OPlanesIntersect", which is the collection of lines created by IntersectPath of Planes.
After that, I can get a collection of Points named "LineIntersects" by Intersect those lines in "OPlanesIntersect".
Not all these points is useful for me, only those points on at least three lines form a vertex of the solid. So, i need to get those points, the problem is how? the points in "LineIntersects" have duplicates, seems that i only need to count the frequency, and get those with frequency count more than 3.
I tried the command Frequency(LineIntersects), but it does not work, and Sort(LineIntersects) does not seem to return result as i expect.
ggb file share link:https://www.geogebra.org/m/ws5bdcma