In geometry, the gyroelongated square cupola is one of the Johnson solids (J<sub>23</sub>). As the name suggests, it can be constructed by gyroelongating a square cupola (J<sub>4</sub>) by attaching an octagonal antiprism to its base. It can also be seen as a gyroelongated square bicupola (J<sub>45</sub>) with one square bicupola removed.
250px|thumb|left|An unfolded gyroelongated square cupola, faces colored by symmetry
250px|thumb|left|An unfolded gyroelongated square cupola
thumb|3D model of a gyroelongated square cupola
Area and volume
The surface area is
:<math>A=\left(7+2\sqrt{2}+5\sqrt{3}\right)a^2\approx 18.4886811...a^2.</math>
The volume is the sum of the volume of a square cupola and the volume of an octagonal prism,
:<math>V=\left(1+\frac{2}{3}\sqrt{2} + \frac{2}{3}\sqrt{4+2\sqrt{2}+2\sqrt{146+103\sqrt{2}\right)a^3</math> <math>\approx6.2107658...a^3.</math>
Dual polyhedron
The dual of the gyroelongated square cupola has 20 faces: 8 kites, 4 rhombi, and 8 pentagons.
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!Dual gyroelongated square cupola
!Net of dual
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