When I want to make a regular polygonal prism in FreeCAD, I do the following:
Step 1: Make a polygon using the Draft Toolbar's Wire tool.
This is easiest if you make the polygon centered around one of the axes(for example, the Z-axis) and parallel to one of the coordinate grids(for example, the xy-plane).
Under these citeria, the corners of a regular n-gon are defined by the polar cooridinates r, 360m/n degrees where r is the n-gon's out radius and m is any integer between one and n.Here
is the polar to rectangular calculator I use to convert the polar coordinates into the rectangular coordinates the wire tool requires.
For a heptagonal prism centered at the origin with its axis of sysmetry coinciding with the z-axis, you would use:
r, 360m/7 degrees converted to rectangular for the x and y values.
a constant h/2 for the z values, where h is the desired height of the prism.
Step 2: Use the Upgrade option from the Draft menu to turn the polygonal wire into a polygonal face.
Step 3: Use the extrude tool on the polygonal face to produce the prism.
Continueing from the above example, you would chose to extrude in the negative z-direction for h units.
Creating a prism aligned with the x or y-axis would be as simple as switching around the numbers, and centering it somewhere other than the origin could be done simply by adding the offsets to the number entered into the wire tool.
Creating a prism with a skewed axis is beyond my knowledge however.
Cutting up the solid can somewhat difficult, especially since FreeCAD does not, as far as I know, have a split solid tool. However, I have found that creating wires, revolving them to form surfaces, and extruding surfaces to produce solids that engulf large segments of puzzle's base solid goes a long way in creating things that can be cut from or intersected with the base solid to form individual puzzle pieces. The Edit menu's duplicate and placement options are also useful for quickly making extras of a complicated part and preparing the puzzle for stl export, and the Drafting toolbar's mirror tool is useful for making chiral copies.
Also, FreeCAD's Forum
on SourceForge is filled with people willing to help out others on how to do different things in FreeCAD.