Graphing 3D shapes

I will go ahead and apologize right away for my general naivete. This is not a homework problem or anything like that, it's a personal project that my limited mathematics knowledge is, well, limiting. I'm not even sure if this is the right sub-section of the forum, so please feel free to re-direct me.

I'm going to try and describe my intention the best that I can, I hope this information is sufficient to answer my question:

I'm trying to find an equation, which I assume will be a function, which results in a set of all points that form a particular shape. The shape is two equilateral triangles, standing "up" and leaning on each other's bases. I did my best to draw a tilted version of it here.

There are four points on the graph that form the boundaries of the shape. The actual numerical values are arbitrary except for their proportions to each other (X,Y,Z): (0,0,0), (5,10,10), (5,-10,10) and (10,0,0)

When X=0, Y and Z=0. For every point that X moves from 0 to 5, there are two points that occur on the Y and Z axis: (Y=2X,-2X and Z=2X). Then from every point that X moves from 5-10, the y/z points are "mirrored" in the opposite direction.

The other way I can think to describe the axis are in comparison to each other:
The X set goes from 0-max linearly. The Y set "expands" outward in a Y^-Y relationship from 0-max halfway through the X set, and then from max-0 in the back half. The Z set is a single set of points from 0-max and max-0.

Once again I excuse myself for general illiteracy in this language, and I would greatly appreciate anyone who would take some time to help me out.