“Snub icosidodecadodecahedron”的意思、由来-开放百科全书

词条

Snub icosidodecadodecahedron

释义

In geometry, the snub icosidodecadodecahedron is a nonconvex uniform polyhedron, indexed as U₄₆.

As the name indicates, it belongs to the family of snub polyhedra.

Cartesian coordinates

Cartesian coordinates for the vertices of a snub icosidodecadodecahedron are all the even permutations of

(±2α, ±2γ, ±2β),

(±(α+β/τ+γτ), ±(-ατ+β+γ/τ), ±(α/τ+βτ-γ)),

(±(-α/τ+βτ+γ), ±(-α+β/τ-γτ), ±(ατ+β-γ/τ)),

(±(-α/τ+βτ-γ), ±(α-β/τ-γτ), ±(ατ+β+γ/τ)) and

(±(α+β/τ-γτ), ±(ατ-β+γ/τ), ±(α/τ+βτ+γ)),

with an even number of plus signs, where

α = ρ+1 = ρ³,

β = τ²ρ²+τ²ρ+τ = τ²ρ⁴+τ,

γ = ρ²+τρ,

and where τ = (1+{{radic|5}})/2 is the golden mean and

ρ is the real solution to ρ³=ρ+1, or approximately 1.3247180.

ρ is called the plastic constant.

Taking the odd permutations of the above coordinates with an odd number of plus signs gives another form, the enantiomorph of the other one.

{{Uniform polyhedra db|Uniform dual polyhedron stat table|Sided}}

The medial hexagonal hexecontahedron is a nonconvex isohedral polyhedron. It is the dual of the uniform snub icosidodecadodecahedron.

{{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}}

{{mathworld | urlname = SnubIcosidodecadodecahedron| title = Snub icosidodecadodecahedron}}
{{mathworld | urlname = MedialHexagonalHexecontahedron| title =Medial hexagonal hexecontahedron}}

1 : Uniform polyhedra

随便看

开放百科全书收录14589846条英语、德语、日语等多语种百科知识，基本涵盖了大多数领域的百科知识，是一部内容自由、开放的电子版国际百科全书。