Am trying to construct a pyramid tree.
In a r dimensional space, A pyramid tree is made of 2*r pyramids.
For example in a 2 D space, we will have four pyramids (four triangles). The triangles would all share it's vertex at origin and have the four bases as the four bounding lines of the space as shown in the below image
The same pyramid in the 3 D space would be similar as above but instead of the base being a line would be a plane and the structure itself would be a pyramid. Generally in a r dimensional space, the sides of the pyramid would be a (r-1) dimensional hyperplane.
My question is, In case of 2-D, the line equation of the sides of the Pyramid are straight-forward. (x=y and x =-y). But how do we find the equation of the sides of the pyramid in an arbitrary dimensional space.
Any help posted or any pointers to material I should start studying will greatly be appreciated.
Thanks in advance,