Gyroelongated Square Dipyramid Calculator

Name: Gyroelongated Square Dipyramid - Geometry Calculator
Author: Jürgen Kummer

Calculations at a gyroelongated square dipyramid, the Johnson solid J₁₇. This is a gyroelongated square pyramid, with another square pyramid attached to the other side. The gyroelongated square dipyramid is an antiprism between two Johnson square pyramids.
Enter one value and choose the number of decimal places. Then click Calculate.

Formulas:

h = (\sqrt{1 - \frac{1}{2 + \sqrt{2}}} + \sqrt{2}) \cdot a

A = 4 \cdot \sqrt{3} \cdot a^{2}

V = \frac{\sqrt{2} + \sqrt{4 + 3 \sqrt{2}}}{3} \cdot a^{3}

Edge length and height have the same unit (e.g. meter), the area has this unit squared (e.g. square meter), the volume has this unit to the power of three (e.g. cubic meter). A/V has this unit ^-1.

The gyroelongated square bipyramid is the last modified pyramid in the list of Johnson solids. This solid, J17, is based on the gyroelongated square pyramid, the Johnson solid J₁₀. The related solid J₁₁ is the gyroelongated pentagonal pyramid. If this is extended to form the gyroelongated pentagonal bipyramid, the result is the icosahedron, which is already a Platonic solid.

Adding an extra pyramid does not increase the mirror symmetry. In this regard, the gyroelongated square bipyramid shares the same symmetry properties as the gyroelongated square pyramid. This is because the twist prevents the formation of an additional plane of symmetry that would otherwise reflect one pyramid onto the other. Due to the twist, the shape also lacks point symmetry. However, it possesses higher rotational symmetry, featuring additional axes of rotation for 180-degree turns and multiples thereof. Furthermore, the gyroelongated square bipyramid has an eight-fold rotary-reflection axis along its vertical axis. This means that the solid maps onto itself following a 45-degree rotation combined with a reflection across a plane perpendicular to that axis.
The gyroelongated square bipyramid serves as a model for certain chemical structures.

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