Cam turned a cylindrical box and lid from a single 90mm sided cube. The box retains three of the cube’s faces, which become almond shaped facets on the completed box.
Start by mounting opposing corners of the cube in jam chucks that fit the ‘pyramid corners’ of the cube. (The jam chucks can be made by cutting a 60 degree angle from the long edge of a slat, then triangulate equilaterally from this beveled edge and cut. Glue three pieces together, then round and spigot, to create a three sided recess jam chuck that fits any cube’s corners.)
Use a bowl gouge to round the mounted cube blank down to 100mm diameter.
Create a 45mm or 60mm diameter spigot on the headstock side. From the point where the three cube faces meet the already turned 100mm diameter, to towards the headstock, turn down to 80mm. This portion will become the lid.
From the headstock side of the 100mm diameter, measure 25mm towards the tailstock and part off. Remount using the 45mm or 60mm spigot into chuck jaws. Using callipers measure a 65mm diameter circle in the tailstock side face, which will become the box cavity. Square the rim and hollow the box cavity 24mm straight in. Create a 90 degree corner to a flat base.
For the outer sides of the box, create a gentle curve from the box rim to the 80mm portion. At this point, using a 2mm parting tool, cut the box base off the blank leaving the lid portion still mounted to the lathe.
Square this face, then concave the inside of the lid 5mm deep and 65mm in diameter. The lid has a protruding lip that fits into the box recess. Use a skew to incrementally remove the lid’s rim outer edge, and test by bringing the box up to it, until there is a precise fit.
Mount the box base on the lid and fix with masking tape for a secure but temporary attachment, and bring the tailstock up for additional support.
Use a bowl gouge to shape the lid’s top surface up towards the mounted spigot. Then shape the box base outer. The three flat facets should remain in an almond shape.
Remove the masking tape and reverse the lid into a jam chuck in order to turn off the previously mounted spigot, and shape the top of the lid. Bring the tail stock up. Use a bowl gouge to shape the lid into a curve, using the remaining cube pyramid to make the lids knob.
The result is an elegant box to fit the butterfly taonga. Retaining portions of the cubes outer faces through the turning results in the unique three-way symmetry of this box’s design.