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Elongated triangular orthobicupola : ウィキペディア英語版
Elongated triangular orthobicupola

In geometry, the elongated triangular orthobicupola is one of the Johnson solids (''J''35). As the name suggests, it can be constructed by elongating a triangular orthobicupola (''J''27) by inserting a hexagonal prism between its two halves. The resulting solid is superficially similar to the rhombicuboctahedron (one of the Archimedean solids), with the difference that it has threefold rotational symmetry about its axis instead of fourfold symmetry.
== Volume ==
The volume of ''J''35 can be calculated as follows:
''J''35 consists of 2 cupolae and hexagonal prism.
The two cupolae makes 1 cuboctahedron = 8 tetrahedra + 6 half-octahedra.
1 octahedron = 4 tetrahedra, so total we have 20 tetrahedra.
What is the volume of a tetrahedron?
Construct a tetrahedron having vertices in common with alternate vertices of a
cube (of side \frac = \frac V_ = \frac \frac^3} = \frac
The hexagonal prism is more straightforward. The hexagon has area 6 \frac, so
V_ = \frac
Finally
V_ + V_ =
\frac + \frac
numerical value:
V_{J_{35}} = 4.9550988153084743549606507192748

抄文引用元・出典: フリー百科事典『 ウィキペディア(Wikipedia)
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