Abstract
A regular triangular pyramid which has height h and an equilateral triangle of side-length 1 can be held by the circle if h > 0.277 . . ..
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Tanoue, Y. Regular triangular pyramids held by a circle. J. Geom. 94, 151–157 (2009). https://doi.org/10.1007/s00022-009-0003-9
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DOI: https://doi.org/10.1007/s00022-009-0003-9