Hexagonal Albert-prism

Geometry Level pending

Albert was going to be famous by coming up with a new family of solids made of regular polygons. There were going to be prisms, anti-prisms, and Albert-prisms. Each Albert-prism would have two identical large regular polygons for the end faces, both attended by a row of equilateral triangles. The two rows would meet at the distant vertices and by doing would create a line square faces. However, when he tried to make a paper model of the hexagonal Albert-prism, the model kept warping.

In order for the model to work, he should have used a different quadrilateral in place of a square. Find the smallest internal angle of this quadrilateral in degrees.

Give your answer to 3 decimal places.

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