TL;DR
This paper explores right quadrilateral-based prisms with all edges, face diagonals, and space diagonals as integers, identifying specific cases with isosceles trapezium and parallelogram bases.
Contribution
It provides new examples of perfect right quadrilateral prisms with integer edges and diagonals, and rules out solutions for certain base shapes.
Findings
Examples found with isosceles trapezium and parallelogram bases.
No solutions for kites or rhombus bases.
Advances understanding of integer-length right quadrilateral prisms.
Abstract
We consider right prisms with horizontal quadrilateral bases and tops, and vertical rectangular sides. We look for examples where all the edges, face diagonals and space diagonals are integers. We find examples when the base is an isosceles trapezium and a parallelogram, but no solution for a kite or rhombus.
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