On 2016-09-14 17:45, James Buddenhagen wrote:

Haha -- that is an endearing name :) . Do you happen to have an off file for that? I'm still trying to figure out what it is!

You mean like Graphics3D@Polygon@{{{-(1/2), -(1/2), -(1/(2 2^(1/4)))}, {-(1/2), 1/ 2, -(1/(2 2^(1/4)))}, {-(1/2), 0, 1/4 (-2^(3/4) - 2 Sqrt[3])}}, {{1/2, 0, 1/4 (-2^(3/4) - 2 Sqrt[3])}, {1/2, 1/2, -(1/(2 2^(1/4)))}, {1/ 2, -(1/2), -(1/(2 2^(1/4)))}}, {{-(1/2), 0, 1/4 (-2^(3/4) - 2 Sqrt[3])}, {-(1/2), 1/2, -(1/(2 2^(1/4)))}, {1/2, 1/2, -(1/(2 2^(1/4)))}, {1/2, 0, 1/4 (-2^(3/4) - 2 Sqrt[3])}}, {{-(1/2), -(1/2), -(1/( 2 2^(1/4)))}, {-(1/2), 0, 1/4 (-2^(3/4) - 2 Sqrt[3])}, {1/2, 0, 1/4 (-2^(3/4) - 2 Sqrt[3])}, {1/2, -(1/2), -(1/(2 2^(1/4)))}}, {{1/ 2, 1/2, -(1/(2 2^(1/4)))}, {0, 1/Sqrt[2], 1/(2 2^(1/4))}, {1/Sqrt[ 2], 0, 1/(2 2^(1/4))}}, {{-(1/2), 1/ 2, -(1/(2 2^(1/4)))}, {-(1/Sqrt[2]), 0, 1/(2 2^(1/4))}, {0, 1/Sqrt[ 2], 1/(2 2^(1/4))}}, {{-(1/2), -(1/2), -(1/(2 2^(1/4)))}, {0, -(1/ Sqrt[2]), 1/(2 2^(1/4))}, {-(1/Sqrt[2]), 0, 1/(2 2^(1/4))}}, {{1/ 2, -(1/2), -(1/(2 2^(1/4)))}, {1/Sqrt[2], 0, 1/( 2 2^(1/4))}, {0, -(1/Sqrt[2]), 1/(2 2^(1/4))}}, {{1/2, 1/ 2, -(1/(2 2^(1/4)))}, {-(1/2), 1/2, -(1/(2 2^(1/4)))}, {0, 1/Sqrt[ 2], 1/(2 2^(1/4))}}, {{-(1/2), 1/ 2, -(1/(2 2^(1/4)))}, {-(1/2), -(1/2), -(1/(2 2^(1/4)))}, {-(1/ Sqrt[2]), 0, 1/( 2 2^(1/4))}}, {{-(1/2), -(1/2), -(1/(2 2^(1/4)))}, {1/ 2, -(1/2), -(1/(2 2^(1/4)))}, {0, -(1/Sqrt[2]), 1/( 2 2^(1/4))}}, {{1/2, -(1/2), -(1/(2 2^(1/4)))}, {1/2, 1/ 2, -(1/(2 2^(1/4)))}, {1/Sqrt[2], 0, 1/( 2 2^(1/4))}}, {{-(1/(2 Sqrt[2])), -(1/(2 Sqrt[2])), 1/4 (2^(3/4) + 2 Sqrt[3])}, {-(1/Sqrt[2]), 0, 1/( 2 2^(1/4))}, {0, -(1/Sqrt[2]), 1/(2 2^(1/4))}}, {{1/Sqrt[2], 0, 1/( 2 2^(1/4))}, {0, 1/Sqrt[2], 1/(2 2^(1/4))}, {1/(2 Sqrt[2]), 1/( 2 Sqrt[2]), 1/4 (2^(3/4) + 2 Sqrt[3])}}, {{1/(2 Sqrt[2]), 1/( 2 Sqrt[2]), 1/4 (2^(3/4) + 2 Sqrt[3])}, {0, 1/Sqrt[2], 1/( 2 2^(1/4))}, {-(1/Sqrt[2]), 0, 1/( 2 2^(1/4))}, {-(1/(2 Sqrt[2])), -(1/(2 Sqrt[2])), 1/4 (2^(3/4) + 2 Sqrt[3])}}, {{1/Sqrt[2], 0, 1/(2 2^(1/4))}, {1/( 2 Sqrt[2]), 1/(2 Sqrt[2]), 1/4 (2^(3/4) + 2 Sqrt[3])}, {-(1/(2 Sqrt[2])), -(1/(2 Sqrt[2])), 1/4 (2^(3/4) + 2 Sqrt[3])}, {0, -(1/Sqrt[2]), 1/(2 2^(1/4))}}} ? A fastigium is apparently just a triangular prism with square sides. This is two of them endcapping a square antiprism. --rwg Johnson had to eschew nonconvex solids because they're infinitudinous, narrowly excluding such gems as bilunagyrobicupola.

On Wed, Sep 14, 2016 at 4:10 AM, Bill Gosper <billgosper@gmail.com> wrote:

...

is nonconvex, but the name is irresistible. gosper.org/gyroelongatedbifastigium.png Resistince is futile. --rwg