# 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 layers.

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.

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