Square orthobicupola

In geometry, the square orthobicupola is a Johnson solid constructed by two square cupolas base-to-base.

File:J28 square orthobicupola.stl

3D model of a square orthobicupola

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 $J_{28}$.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 $A$ of a total sum of its area's faces, eight equilateral triangles and two squares. Its volume $V$ is twice that of the square cupola's volume. With the edge length $a$, they are:Template:R $$\begin{array}{rl}A& =(2\cdot \sqrt{3}+10)a^2\approx 13.464a^2,\\ V& =(2+\frac{4\sqrt{2}}{3})a^3\approx 3.886a^3.\end{array}$$

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

External links

• Template:Mathworld2

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