Nexus Network Journal

, Volume 20, Issue 1, pp 267–281 | Cite as

Double Orthogonal Projection of Four-Dimensional Objects onto Two Perpendicular Three-Dimensional Spaces

  • Michal Zamboj
Geometer’s Angle


A method of visualization of four-dimensional objects using a double orthogonal parallel projection onto two orthogonal three-dimensional spaces is proposed. A synthetic approach, with the use of basic descriptive geometry tools of Monge’s projection in interactive 3D graphical software, is taken. Descriptive constructions of projections of points, lines, planes and three-dimensional spaces are shown. Methods of measuring true lengths of segments and rotating projections of objects into the modeling space are described. The focus lies on improving the spatial ability and understanding of the four-dimensional space. An example of a construction is carried out on a model of tesseract. All the constructions are analogies of constructions in Monge’s projection of a three-dimensional space. With advantages of interactive computer graphics, the constructions are easy to perform, and objects are easy to manipulate with.


Four-dimensional visualization Multidimensional descriptive geometry Monge’s projection Tesseract 



The work was supported by the grant SVV 2017 No. 260454. I also wish to thank Lukas Krump (Charles University) for valuable comments on preliminary versions of the text.

Supplementary material

4_2017_368_MOESM1_ESM.ggb (43 kb)
Supplementary material 1 (GGB 44 kb)


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Copyright information

© Kim Williams Books, Turin 2018

Authors and Affiliations

  1. 1.Faculty of Mathematics and PhysicsCharles UniversityPrague 8Czech Republic

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