There exist several kirigami, or non-developable folded plate patterns that share the most useful properties of the widely-used Miura-ori pattern, namely rigid-foldability, a tessellated unit geometry, and constituent elements composed of a single parallelogram plate. This paper first presents parametrisations of five such patterns, two cube-type and three eggbox-type, consistent with that previously developed for Miura-type patterns. For each pattern, the parametrisation establishes relationships between crease pattern, volumetric, and kinematic parameters. Along with the Miura-type patterns, these geometries form a set termed parallelogram-plate folded geometries and together they suggest a range of interesting structural engineering applications. This paper discusses two applications specifically enabled by the new parametrisations: space frame synthesis and hierarchical sandwich panels.
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