The authors redefine and generalize the so-called relative ratio of compactness of solid with respect to sphere and cube introduced by Mahdavi and Gurtekin. The authors propose such new indicators as a relative ratio of solid compactness in the shape of a prism-shaped solid related to a cuboid with a square base and a given height (e.g. the height of the analyzed storey), a solid compactness indicator defined for the basis of the prism relative to the square. They introduce also other indicators: a relative defect of the perimeter and area. The test of indicators formulated and described in the paper was carried out in two groups of buildings: existing (spotted locally) and those whose designs can be found in the selected catalog available on the website. In addition to the compactness ratios calculated for existing and designed buildings, an analysis of the size of the indicators for the adopted building research models was made. Proposed indicators allow for a description of the compactness of the building model with an indication of the deviation from the real ideal solid. The introduced geometric determinants of solids may be useful in the initial phase of searching for satisfactory design solutions.

Changes taking currently place in upbringing and teaching, force teachers to constantly search for newer methods of transmitting knowledge to their students. Young people beginning their studies are brought up in different ways of gaining recognition skills than they were a few years ago. Children play with blocks, building various structures and learning the shapes and features of single blocks, but they must be able to imagine the overall effects in their work. During our geometry classes, we refer to wooden models of solids like pyramids and prisms, so that building models from blocks becomes more natural and less hard. With this in mind, we came up with an idea to prepare a number of models that students could cut from a single piece of paper and then fold it to confront a 2D illustration with the corresponding 3D model. In this paper, assumptions according to the model that we made, as well as solutions and some examples, are presented.

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