Bridged Trispheres and Tetraspheres
If we join the sets of bridged trispheres and tetraspheres we get 94 pieces with a
total volume of 368 spheres. This is a perfect set to construct different boxes. We
have to solve the equation
a*(2b-1)(2c-1)-((2b-1)(2c-1)-1)/2 = 368 for 2 ≤ a ≤ b ≤ c
a, b, c are the numbers of spheres touching the faces of the boxes in
each direction. We get four solutions and all boxes are solvable. I used acrylic panes to stabilize the constructions.
Otherwise flat pieces parallel
to the faces could easily fall apart. If the construction isn't finished it must be possible
to shift the panes, because sometimes the construction must be pulled apart a little
to insert further pieces. The box with a=4, b=4, c=8 shown above was filled using a variable
frame of card board and at last moved to the sturdy acrylic box. Click the pictures to see the
The 3x4x11 box
The 2x4x18 box
The 2x3x25 box
A dam with four layers of size 7x18, 6x17, 5x16, and 4x15 can also be made with the combined set.
All pieces without the piece shaped like a size 2 tetrahedron can be used to create
a large tetrahedron of size 12. Beside the hexagonal layers
of the solution starting with the top layer it seems to be easier
to use the orthogonal layers starting with the right edge at the bottom.