Square orthobicupola
Template:Short description {{#invoke:Infobox|infobox}}Template:Template other </math> |vertex_config= <math> 8 \times (3^2 \times 4^2) + 8 \times (3 \times 4^3) </math> |properties=convex |net=square orthobicupola flat.svg }}
In geometry, the square orthobicupola is a Johnson solid constructed by two square cupolas base-to-base.
Construction
The square orthobicupola is started by attaching two square cupolae onto their bases.Template:R The resulting polyhedron consisted of eight equilateral triangles and ten squares, having eighteen faces in total, as well as thirty-two edges and sixteen vertices. A convex polyhedron in which the faces are all regular polygons is a Johnson solid, and the square orthobicupola is one of them, enumerated as twenty-eighth Johnson solid <math> J_{28} </math>.Template:R This construction is similar to the next one, the square gyrobicupola, which is twisted one of the cupolae around 45°.Template:R
Properties
The square orthobicupola has surface area <math> A </math> of a total sum of its area's faces, eight equilateral triangles and two squares. Its volume <math> V </math> is twice that of the square cupola's volume. With the edge length <math> a </math>, they are:Template:R <math display="block"> \begin{align}
A &= \left(2 \cdot \sqrt{3} + 10\right)a^2 \approx 13.464a^2, \\
V &= \left(2+\frac{4\sqrt{2}}{3}\right)a^3 \approx 3.886a^3.
\end{align} </math>
The square orthobicupola has an axis of symmetry (a line passing through the center of two cupolas at their top) that rotates around one-, two-, and third-fourth of a full turn, and is reflected over the plane so the appearance remains symmetrical. The solid is also symmetrical by reflection over three mutually orthogonal planes.Template:R