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Seven-Sided Polyhedron

For the two-sided coloring, used (in the Graphics3D[] command):


And exported to .stl with

Export["Heptahedron.stl", g, "STL"]

Checked in blender: all works.

Density of Materials (Stephanie, 9 Feb 11)

Density of ABS Plastic: 1.04 g/cm^3

Liquid we float the ABS Plastic in must be more dense than 1.04 g/cm^3

Possible Substances Researched:

Milk 1.04-1.05 g/cm^3 (possibility)

Iodine 4.927 g/cm^3

Salt Water 1.025 + g/cm^3

Glycerin 1.261 g/cm^3 --> This is the final decision. We will float the objects in glycerin.

Objects we will 3D Print

Click on each image to see it full-size. Copy full-size with right-click Save Link As on the file name on that full-size page.

Rhombic Dodecahedron
Heptahedron585. This was a miscalculation. The one we printed is a bit taller. See images below.

InSphere Center at the Center of Gravity

These images show that the faces of the polyhedron are tangent to the Chebyshev sphere (the largest enclosed sphere), and so equidistant from the sphere center (known as its incenter). For this example, we can argue from symmetry that the incenter is the same as the center of mass/gravity.

Fair Heptahedron: View 1
Fair Heptahedron: View 2
Fair Heptahedron: View 3

Also the bipyramids have the same property. See the page and image.

Truncated Cube (6Apr11)

Truncated Cube