Great deltoidal icositetrahedron

In geometry, the great deltoidal icositetrahedron (or great sagittal disdodecahedron) is the dual of the nonconvex great rhombicuboctahedron. Its faces are darts. Part of each dart lies inside the solid, hence is invisible in solid models.

Great deltoidal icositetrahedron

Type	Star polyhedron
Face
Elements	F = 24, E = 48 V = 26 (χ = 2)
Symmetry group	O_h, [4,3], *432
Index references	DU₁₇
dual polyhedron	Nonconvex great rhombicuboctahedron

Proportions

Faces have three angles of $\arccos({\frac {1}{2}}+{\frac {1}{4}}{\sqrt {2}})\approx 31.399\,714\,809\,92^{\circ }$ and one of $360^{\circ }-\arccos(-{\frac {1}{4}}+{\frac {1}{8}}{\sqrt {2}})\approx 265.800\,855\,570\,24^{\circ }$ . Its dihedral angles equal $\arccos({\frac {-7+4{\sqrt {2}}}{17}})\approx 94.531\,580\,798\,20^{\circ }$ . The ratio between the lengths of the long edges and the short ones equals $2+{\frac {1}{2}}{\sqrt {2}}\approx 2.707\,106\,781\,19$ .

gollark: I just download anything interesting on YT etc. and all the stuff from some youtubers.

gollark: I have something like 120GB of random video stuff versus 5GB of music, 3GB of book stuff and 1GB of notes/personal pictures.

gollark: Presumably they can just run everything possible off 12V, and simplify cabling.

gollark: Boards will apparently have buck converters for 5V/3.3V.

gollark: There's that 4-pin connector for extra CPU power, which is 12V, so I assume they mostly use that.

References

Wenninger, Magnus (1983), Dual Models, Cambridge University Press, ISBN 978-0-521-54325-5, MR 0730208

External links

Weisstein, Eric W. "Great Deltoidal Icositetrahedron". MathWorld.

This article is issued from Wikipedia. The text is licensed under Creative Commons - Attribution - Sharealike. Additional terms may apply for the media files.