“Bilunabirotunda”的意思、由来-开放百科全书

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Bilunabirotunda

释义

Cartesian coordinates
Related polyhedra and honeycombs
External links

{{cleanup HTML|date=February 2019}}{{Infobox polyhedron
|image=Bilunabirotunda.png
|type=Johnson
J₉₀ - J₉₁ - J₉₂
|faces=2x4 triangles
2 squares
4 pentagons
|edges=26
|vertices=14
|symmetry=D_2h|
|vertex_config=4(3.5²)
8(3.4.3.5)
2(3.5.3.5)
|dual=-
|properties=convex
|net=Johnson solid 91 net.png
}}

In geometry, the bilunabirotunda is one of the Johnson solids (J₉₁).

It is one of the elementary Johnson solids, which do not arise from "cut and paste" manipulations of the Platonic and Archimedean solids. However, it does have a strong relationship to the icosidodecahedron, an Archimedean solid. Either one of the two clusters of two pentagons and two triangles can be aligned with a congruent patch of faces on the icosidodecahedron. If two bilunabirotundae are aligned this way on opposite sides of the icosidodecahedron, then two vertices from the bilunabirotundae will meet in the very center of the icosidodecahedron.

The other two clusters of faces of the bilunabirotunda, each with one square and two triangles, can be aligned with a congruent patch of faces on the rhombicosidodecahedron. If two bilunabirotundae are aligned this way on opposite sides of the rhombicosidodecahedron, then a cube can be put between the bilunabirotundae at the very center of the rhombicosidodecahedron.

Cartesian coordinates

The following define the vertices of a bilunabirotunda centered at the origin with edge length 1:

where is the golden ratio.

Related polyhedra and honeycombs

{{Further|Regular_dodecahedron#Space_filling_with_cube_and_bilunabirotunda}}

Six bilunabirotundae can be augmented around a cube with pyritohedral symmetry. B. M. Stewart labeled this six-bilunabirotunda model as 6J₉₁(P₄).^[1]

The bilunabirotunda can be used with the regular dodecahedron and cube as a space-filling honeycomb.

Spacefilling honeycomb	6 bilunabirotundae around a cube

External links

1. ^B. M. Stewart, Adventures Among the Toroids: A Study of Quasi-Convex, Aplanar, Tunneled Orientable Polyhedra of Positive Genus Having Regular Faces With Disjoint Interiors (1980) {{ISBN|978-0686119364}}, (page 127, 2nd ed.) polyhedron 6J₉₁(P₄).

{{Mathworld2 | urlname2 = JohnsonSolid | title2 = Johnson solid | urlname =Bilunabirotunda| title = Bilunabirotunda}}
Miracle Spacefilling (Dodecahedron&Cube&Johnson solid No.91)

1 : Johnson solids

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