I happen to have a copy of Stewart Coffin’s Design Notes (printed by John Rausch) that shows this very cool design as having 8 solutions for packing all pieces in the box while only one solution exists for packing the pieces in the box without the lone block!
There are many other shapes possible with this set as well..Stewart found three other challenges for creating a pyramid shape:
Square Base - 3 solutions
Rectangular Base - One solution
Regular Tetrahedron (omit one piece) - One Solution - ‘the most difficult challenge’
Here are some of the other shapes that are possible:
Bug - 8 blocks
Volcano - 13 blocks
Tower - 14 blocks
Ridge - 14 blocks
Rock Pile
Muffin
Skewed Hex
Swiss Chalet
As a side note: Stewart appears to have toyed with the idea of an improved version in 1983 showing an alternate solution for making a cube by substituting a piece.
It appears this version would have also made the three different pyramid shapes along with a ‘Projecting Block’ and ‘Christmas Tree’…
Here’s Stewart’s description:
“This introduces a large family of puzzles made by joining polyhedral blocks together different ways, in this case using edge-beveled cubes (or to put it another way truncated rhombic dodecahedrons).
Strange as it may seem, they pack snugly and neatly into the cubic box with or without the single block. They will also form several other symmetrical assemblies, only a few of which are shown. Use your imagination.”
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