This paper describes in a rather epistemological way the genesis of a class of three-dimensional objects that feature views of flat figures organized with the seven pieces of the Chinese Tangram puzzle, when looked at from certain privileged directions, and therefore called tangramoids. A subclass is considered here, where the objects are structures assembled from plane, generally opaque, polygons. The objects can either be closed (irregular polyhedra) or open (when not all edges of polygons are adjacent to others). The tangramoids discussed here are further limited to feature plan views of the generic square Tangram figure, and of Tangram figures involving a square made of the five smaller pieces. Finally, mainly instances displaying a characteristically pleasing symmetry are discussed. They are represented in space as sculptures or in the plane as graphical works including interactive computer renderings.