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Tetrahedral Stellation of Dodecahedron 1
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This is also the shape you get if inscribe a cube in a dodecahedron, cut off the 6 "tents" to leave just the inscribed cube, then flip the tents over and extract them from the cube faces instead. My dodecahedral shape-shifter demonstrates this.

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Tetrahedral Stellation of Dodecahedron 1
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