The research problem of the article refers to the question of the sense of using concrete prefabrication to create a new quality of architecture for single-family houses. Known and referenced projects from the past — from the period of early architectural Rationalism (Modernism and Functionalism) — seem appropriate to show, recall and update the idea of concrete prefabrication of single-family houses in the present day. This point of reference, having its source in the vision of the housing revolution from the beginning of the 20th century, can today be the subject of direct references and the search for further variants of rational patterns of modern prefabrication of single-family houses. The article is based on the most important items from the beginnings of concrete prefabrication technology, including Vers une architecture (1923) by Le Corbusier and articles and manuscripts by Walter Gropius following new concepts in German construction. Newer items include the Gilbert Herbert’s text that summarizes the heritage of Gropius’ prefabrication entitled The Dream of the Factory Made House by Walter Gropius and Konrad Wachsmann (1984).
The research method was the analysis of selected historical and contemporary houses built either in whole or in part in the precast concrete technology (a multiple-case study). The presentation of new examples shows the possibility of adapting the rational ideas and aesthetics of architecture from the early 20th century with the use of the latest concrete technologies. According to the author, the sense of concrete prefabrication in the construction of single-family houses is to return to the idea of ‘developed’ technology rationalization and Modernist architectural aesthetics. Although prefabrication is associated with the domain of economization, modularity, standardization and typification, thanks to advanced technologies, a prefabricated house in the 21st century can be a proof of the multitude of possible configurations.

The paper presents a method of construction of cylindrical and azimuthal equalarea map projections of a triaxial ellipsoid. Equations of a triaxial ellipsoid are a function of reduced coordinates and functions of projections are expressed with use of the normal elliptic integral of the second kind and Jacobian elliptic functions. This solution allows us to use standard methods of solving such integrals and functions. The article also presents functions for the calculation of distortion. The maps illustrate the basic properties of developed map projections. Distortion of areas and lengths are presented on isograms and by Tissot’s indicatrixes with garticules of reduced coordinates. In this paper the author continues his considerations of the application of reduced coordinates to the construction of map projections for equidistant map projections. The developed method can be used in planetary cartography for mapping irregular objects, for which tri-axial ellipsoids have been accepted as reference surfaces. It can also be used to calculate the surface areas of regions located on these objects. The calculations were carried out for a tri-axial ellipsoid with semi-axes a = 267:5 m, b = 147 m, c = 104:5 m accepted as a reference ellipsoid for the Itokawa asteroid.