Modeling and visualizing of the formation of a snub dodecahedron in the AutoCAD system

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The article is devoted to modeling and visualization of the formation of flat-nosed (snub-nosed) dodecahedron (snub dodecahedron). The purpose of the research is to model the snub dodecahedron (flat-nosed dodecahedron) and visualize the process of its formation. The formation of the faces of the flat-nosed dodecahedron consists in the truncation of the edges and vertices of the Platonic dodecahedron with the subsequent rotation of the new faces around their centers. The values of the truncation of the dodecahedron edges, the angle of rotation of the faces and the length of the edge of the flat-nosed dodecahedron are the parameters of three equations composed as the distances between the vertices of triangles located between the faces of the snub dodecahedron. The solution of these equations was carried out by the method of successive approximations. The results of the calculations were used to create an electronic model of the flat-nosed dodecahedron and visualize its formation. The task was generally achieved in the AutoCAD system using programs in the AutoLISP language. Software has been created for calculating the parameters of modeling a snub dodecahedron and visualizing its formation.

About the authors

Victoryna A. Romanova

Peoples’ Friendship University of Russia (RUDN University)

Author for correspondence.

Associate Professor of the Department of Civil Engineering of the Academy of Engineering

6 Miklukho-Maklaya St, Moscow, 117198, Russian Federation

Stanislav V. Strashnov

Peoples’ Friendship University of Russia (RUDN University)


Associate Professor of the Department of General Education Courses of the Faculty of Russian Language and General Educational Disciplines

6 Miklukho-Maklaya St, Moscow, 117198, Russian Federation


  1. Kiper G. Polyhedra. A historical review. Ankara; 2007.
  2. Cromwell P.R. Polyhedra. Cambridge University Press; 1999.
  3. Krivoshapko S.N. Polyhedra and quasi-polyhedra in architecture of civil and industrial erections. Construction and Reconstruction. 2020;4(90):48–64.
  4. Motulsky R.S. Nacional'naya biblioteka Belarusi: novoe zdanie – novaya koncepciya razvitiya [National Library of Belarus: new building – new development concept]. Minsk; 2007. (In Russ.)
  5. Wenninger M. Polyhedron models. Cambridge University Press; 1971.
  6. Ashkinuz V.G. O chisel polupravil'nyh mnogogrannikov [On the number of semi-control polyhedra]. Mathematical Education. 1957;2(1):107–118. (In Russ.)
  7. Savchenko V. Polupravilnye mnogogranniki [Semicontrolled polyhedral]. Quant. 1979;(1):3. (In Russ.)
  8. Smirnova I.M., Smirnov V.A. Pravilnye, polupravilnyei zvezdchatye mnogogranniki [Correct, semi-control and star polyhedra]. Moscow; MCNMO Publ., 2010. (In Russ.)
  9. Weissbach B., Martini H. On the chiral Archimedean solids. Contrib. Algebra and Geometry. 2002;4:121–133.
  10. Vasilieva V.N. Golden section and golden rectangles when building icosahedron, dodecahedron and archimedean solids based on them. Geometry and Graphics. 2019;7(2):47–55. (In Russ.)
  11. Vasileva V.N. Application of computer technologies in building design by example of original objects of increased complexity. IOP Conf. Ser.: Mater. Sci. Eng. 2017;262:012106.
  12. Rajpoot H.C. Optimum solution of snub dodecahedron (an Archimedean solid) by using HCR's theory of polygon & Newton – Raphson method. Dec. 2014. M.M.M. University of Technology, Gorakhpur-273010 (UP), India.
  13. Ertskina E.B., Korolkova N.N. Geometric modeling in automated design of architectural objects. Geometry and Graphic. 2016;4(2):48–54. (In Russ.)
  14. Romanova V.A. Visualization of regular polyhedrons in the process of their formation. Geometry and Graphics. 2019;7(1):55–67. (In Russ.)
  15. Ivanov V.N., Krivoshapko S.N., Romanova V.A. Bases of development and visualization of objects of analytical surfaces and the prospect of their use in architecture and construction. Geometry and Graphics. 2017;5(4):3–14. (In Russ.)
  16. Ivanov V.N., Romanova V.A. Konstruktsionnye formy prostranstvennykh konstruktsii. Vizualizatsiya poverkhnostei v sistemakh MathCad, AutoCad [Constructive forms of space constructions. Visualization of the surfaces at systems MathCad, AutoCad]. Moscow: ASV Publishing House; 2016. (In Russ.)
  17. Schroeder W.J., Martin K., Lorensen B. The visualization toolkit. Kitware, Inc.; 2003.
  18. Haber R.B. Vizualization techniques for engineering mechanics. Computing Systems in Engineering. 1990;1(1):37–50.
  19. Dupac M., Popirlan C.-I. Web technologies for modelling and visualization in mechanical engineering. 2010. April 1.
  20. Gallagher R.S., Press S. Computer visualization: graphics techniques for engineering and scientific analysis. CRC Press; 1994.
  21. Caha J., Vondrakova A. Fuzzy surface visualization using HSL colour model. Electronic Journal. 2017;2(2):26–42.
  22. Romanova V.A. Vizualizing of semi-regular polyhedrons in AutoCAD environment. Structural Mechanics of Engineering Constructions and Buildings. 2019;15(6):449–457. (In Russ.)
  23. Romanova V.A. Visualizing surface formation of semi-regular polyhedra of Archimedes. Structural Mechanics of Engineering Constructions and Buildings. 2020;16(4):279–289. (In Russ.)

Copyright (c) 2021 Romanova V.A., Strashnov S.V.

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