Английская Википедия:Great dodecicosacron

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Файл:Great dodecicosacron.stl

3D model of a great dodecicosacron

In geometry, the great dodecicosacron (or great dipteral trisicosahedron) is the dual of the great dodecicosahedron (U₆₃). It has 60 intersecting bow-tie-shaped faces.

Proportions

Each face has two angles of <math>\arccos(\frac{3}{4}+\frac{1}{20}\sqrt{5})\approx 30.480\,324\,565\,36^{\circ}</math> and two angles of <math>\arccos(-\frac{5}{12}+\frac{1}{4}\sqrt{5})\approx 81.816\,127\,508\,183^{\circ}</math>. The diagonals of each antiparallelogram intersect at an angle of <math>\arccos(\frac{5}{12}-\frac{1}{60}\sqrt{5})\approx 67.703\,547\,926\,46^{\circ}</math>. The dihedral angle equals <math>\arccos(\frac{-44+3\sqrt{5}}{61})\approx 127.686\,523\,427\,48^{\circ}</math>. The ratio between the lengths of the long edges and the short ones equals <math>\frac{1}{2}+\frac{1}{2}\sqrt{5}</math>, which is the golden ratio. Part of each face lies inside the solid, hence is invisible in solid models.

References

• Шаблон:Citation

External links

• Uniform polyhedra and duals