“Great rhombic triacontahedron”的意思、由来-开放百科全书

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Great rhombic triacontahedron

释义

References
External links

In geometry, the great rhombic triacontahedron is a nonconvex isohedral, isotoxal polyhedron. It is the dual of the great icosidodecahedron (U54). Like the convex rhombic triacontahedron it has 30 rhombic faces, 60 edges and 32 vertices (also 20 on 3-fold and 12 on 5-fold axes).

It can be constructed from the convex solid by expanding the faces by factor of , where is the golden ratio.

This solid is to the compound of great icosahedron and great stellated dodecahedron what the convex one is to the compound of dodecahedron and icosahedron:

The crossing edges in the dual compound are the diagonals of the rhombs.

What resembles an "excavated" rhombic triacontahedron (compare excavated dodecahedron and excavated icosahedron) can be seen within the middle of this compound.

{{multiple image

{{multiple image	perrow=2 \| total_width=400	image1 = Skeleton pair 12-20, size s.png	image2 = Rhombic triacontahedron 1 (convex), size s, pyritohedral.png	image3 = Skeleton pair Gr12 and dual, size s.png	image4 = Rhombic triacontahedron 2 (medial), pyritohedral.png	image5 = Skeleton pair Gr20 and dual, size s.png	image6 = Rhombic triacontahedron 3 (great), pyritohedral.png	footer = Convex, medial and great rhombic triacontahedron on the right (shown with pyritohedral symmetry) and the corresponding dual compounds of regular solids on the left }}
{{multiple image	total_width = 400	image1 = Rhombic triacontahedron 3 (great), size s, 2-fold.png	image2 = Rhombic triacontahedron 3 (great), size s, 3-fold.png	image3 = Rhombic triacontahedron 3 (great), size s, 5-fold.png	footer = Orthographic projections from 2-, 3- and 5-fold axes }}

References

{{Citation | last1=Wenninger | first1=Magnus | author1-link=Magnus Wenninger | title=Dual Models | publisher=Cambridge University Press | isbn=978-0-521-54325-5 | mr= 730208| year=1983}}

External links

{{mathworld | urlname = GreatRhombicTriacontahedron| title =Great rhombic triacontahedron}}
David I. McCooey: animation and measurements
Uniform polyhedra and duals

1 : Dual uniform polyhedra

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