---------- Forwarded message ---------- From: Bill Gosper <billgosper@gmail.com> Date: Fri, Oct 14, 2016 at 12:20 PM Subject: PolyhedronData["TriangularHebesphenorotunda", "Faces"] To: Wolfram Technical Support <support@wolfram.com> <Johnson solid png censored courtesy xmission.com>​ (PolyhedronData["TriangularHebesphenorotunda"] default view hides C3 symmetry.) GraphicsComplex[{{-0.9601329154398749, 0.715228827607169, -0.03894034047821841}, {-0.8187282992850485, 0.1613051767267678, -0.8594117437126204}, ...}] Bleahh. GraphicsComplex[{{-1, 0, 1/32 (Sqrt[3] + 5 Sqrt[15])}, {-(1/2), -(1/(2 Sqrt[3])), -(( 45 + Sqrt[5])/(32 Sqrt[3]))}, {-(1/2), -(Sqrt[3]/2), 1/32 (Sqrt[3] + 5 Sqrt[15])}, {-(1/2), Sqrt[3]/2, 1/32 (Sqrt[3] + 5 Sqrt[15])}, {-(1/2), (2 + Sqrt[5])/( 2 Sqrt[3]), -((13 + Sqrt[5])/(32 Sqrt[3]))}, {0, 1/Sqrt[ 3], -((45 + Sqrt[5])/(32 Sqrt[3]))}, {0, -((3 + Sqrt[5])/( 2 Sqrt[3])), (-29 + 15 Sqrt[5])/(32 Sqrt[3])}, {1/ 2, -(1/(2 Sqrt[3])), -((45 + Sqrt[5])/(32 Sqrt[3]))}, {1/ 2, -(Sqrt[3]/2), 1/32 (Sqrt[3] + 5 Sqrt[15])}, {1/2, Sqrt[3]/2, 1/32 (Sqrt[3] + 5 Sqrt[15])}, {1/2, (2 + Sqrt[5])/( 2 Sqrt[3]), -((13 + Sqrt[5])/(32 Sqrt[3]))}, {1, 0, 1/32 (Sqrt[3] + 5 Sqrt[15])}, {1/4 (-3 - Sqrt[5]), 1/12 (Sqrt[3] - Sqrt[15]), -((13 + Sqrt[5])/(32 Sqrt[3]))}, {1/ 4 (-3 - Sqrt[5]), (3 + Sqrt[5])/(4 Sqrt[3]), (-29 + 15 Sqrt[5])/( 32 Sqrt[3])}, {1/4 (-1 - Sqrt[5]), -((5 + Sqrt[5])/( 4 Sqrt[3])), -((13 + Sqrt[5])/(32 Sqrt[3]))}, {1/ 4 (1 + Sqrt[5]), -((5 + Sqrt[5])/(4 Sqrt[3])), -((13 + Sqrt[5])/( 32 Sqrt[3]))}, {1/4 (3 + Sqrt[5]), 1/12 (Sqrt[3] - Sqrt[15]), -((13 + Sqrt[5])/(32 Sqrt[3]))}, {1/ 4 (3 + Sqrt[5]), (3 + Sqrt[5])/(4 Sqrt[3]), (-29 + 15 Sqrt[5])/( 32 Sqrt[3])}}, Polygon[{{14, 5, 6, 2, 13}, {5, 14, 4}, {14, 1, 4}, {1, 14, 13}, {1, 13, 15, 3}, {15, 13, 2}, {7, 15, 2, 8, 16}, {3, 15, 7}, {9, 3, 7}, {9, 7, 16}, {17, 16, 8}, {9, 16, 17, 12}, {6, 8, 2}, {6, 11, 18, 17, 8}, {18, 12, 17}, {18, 10, 12}, {10, 18, 11}, {5, 4, 10, 11}, {5, 11, 6}, {10, 4, 1, 3, 9, 12}}]] In[776]:= PolyhedronData["TriangularHebesphenorotunda", "Volume"] Out[776]= 5.10875 Bleahh, 5/2 + (7 Sqrt[5])/6 In[458]:= PolyhedronData[%453[[-1]], "Centroid"] Out[458]= {0., 0., 0.} Bleahh. {0, 0, 0}. --rwg

So [ElongatedPentagonalRotunda] just barely won't stand on a square face. --rwg You could use one as a carpenter's level. It must tip over, and again when rotated 180º.

But then why not just keep in your pocket a scrap of copper or PVC pipe?