The Gyroelongated Square Bicupola


The gyroelongated square bicupola is the 45th Johnson solid (J45). It has 24 vertices, 56 edges, and 34 faces (24 equilateral triangles and 10 squares).

The gyroelongated square
bicupola

The gyroelongated square bicupola can be constructed by attaching two square bicupolae to an octagonal antiprism, or equivalently, adding a second square cupola to a gyro­elongated square cupola (J23).

J45 is one of the few Johnson solids that are chiral; it is distinct from its own mirror image:

One enantiomorph of the
gyroelongated square bicupola The other
enantiomorph of the gyroelongated square bicupola

Projections

Here are some views of the gyroelongated square bicupola from various angles:

Projection Description

Top view.

Front view.

11.25° side view.

Coordinates

The Cartesian coordinates of the gyroelongated square bicupola with edge length 2 are:

where H = √((1+√2)(√(1+1/√2)−1)), or approximately 0.860296, is half the height of a hexagonal antiprism of edge length 2.


Last updated 29 May 2018.

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