The base made in Rhino 

From the pyramid pdf plans one shape chosen is copied and rotated 

The two have been exploded and then joined to be one new shape 

This is now extruded upwards to make a solid shape

a hole is now placed in the bottom in order for it to connect to the base object

Two pentagons. one set higher than the other and also the one above is rotated slighty. The two pentagons have been joined using the sweep 2 rails tool. Aflat surface has been drawn between half way up so the two can be split

After spliting it into two, The top half has been moved upwards slighty and rotated. the sweep 2 rails tool has been used a second time to create this shape

Objects placed on base also to show what it will look like