Английская Википедия:Great icosacronic hexecontahedron

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Файл:Great icosacronic hexecontahedron.stl

3D model of a great icosacronic hexecontahedron

In geometry, the great icosacronic hexecontahedron (or great sagittal trisicosahedron) is the dual of the great icosicosidodecahedron. Its faces are darts. A part of each dart lies inside the solid, hence is invisible in solid models.

Proportions

Faces have two angles of <math>\arccos(\frac{3}{4}+\frac{1}{20}\sqrt{5})\approx 30.480\,324\,565\,36^{\circ}</math>, one of <math>\arccos(-\frac{1}{12}+\frac{19}{60}\sqrt{5})\approx 51.335\,802\,942\,83^{\circ}</math> and one of <math>360^{\circ}-\arccos(-\frac{5}{12}+\frac{1}{60}\sqrt{5})\approx 247.703\,547\,926\,46^{\circ}</math>. Its dihedral angles equal <math>\arccos({\frac{-44+3\sqrt{5}}{61}})\approx 127.686\,523\,427\,48^{\circ}</math>. The ratio between the lengths of the long and short edges is <math>\frac{31+5\sqrt{5}}{22}\approx 1.917\,288\,176\,70</math>.

References

• Шаблон:Citation