These are some highlights of my Skewb Square-Antiprism Build.
I had
already seen a 2x2x2 square-antiprism and I wanted to tackle the same
shape with a Skewb basis. I knew it would be a painstaking
process to arrive at a tidy puzzle.
I started
to calculate some angles and measurements, but then I decided to use
Google Sketchup. This is a 1:1 scale model.

I thought about
a slightly truncated version (another time maybe)

Then I worked out the skeleton. I really enjoyed messing around
with these models.

From these two
models I was able to
take the angles of all the internal and external pieces I needed to
cut. I also took length measurements but only as a starting point - as
I made the first of each piece I was able to get actual measurements.
I transferred
the angles onto various reference cards which I used to mark out each
piece.

I made some card extensions to get the feel for the shapes. There are
three extensions each used four times.

The first step in the actual build was to establish the antiprism shape
with
these top and bottom corner extensions...

... and next
were the internal surfaces of the antiprism corners.

I made the four
face extensions as separate units - each with its own base but without
the outer skin. Each was glued on using thin card spacers to centralise
them between the corners.
All that was
left was the "cladding"... I had made the diagonal struts very
slightly oversize and was able correct any errors in angle or offset by
filing.
I glued strengtheners into the larger cladding pieces.
Each
outer piece was hand fitted to get the best outward shape.

Finally the
stickered puzzle...


