moving geometry

publications

this page lists my main publications and other academic outputs in the history of science and geometry, polyhedral theory, mathematics education, and digital modelling in architecture

outputs

journal articles

peer‑reviewed articles in the history of science, geometry, and mathematics education.

  • Viana, Vera. 2026. “Luca Pacioli’s Rhombicuboctahedron: Description, Construction, and Architectural Reception.” Nexus Network Journal. https://link.springer.com/article/10.1007/s00004-026-00885-9
  • Viana, Vera. 2024. “Archimedean Solids in the Fifteenth and Sixteenth Centuries.” Archive for History of Exact Sciences 78 (6): 631–715. https://doi.org/10.1007/s00407-024-00331-7.
  • Đurić, Isidora, Ratko Obradović, Vera Viana, Lidija Krstanović, Bojan Banjac, Jelena Letić, and Nebojša Ralević. 2019. “Algorithm for Image-Based Architectural Element Recognition.” FME Transactions 47 (2): 287–292. https://doi.org/10.5937/fmet1902287d.
  • Viana, Vera. 2018. “From Solid to Plane Tessellations, and Back.” Nexus Network Journal 20 (3): 741–768. https://doi.org/10.1007/s00004-018-0389-5.
  • Viana, Vera. 2014. “Dynamic Geometry Software and Augmented Reality Samples for High School Descriptive Geometry Teaching.” Revista Electrónica de Investigación, Docencia i Creatividad 3: 46–60.
  • Viana, Vera. 2013. “Descriptive Geometry Learning Is No More Threatened by Dynamic Geometry Software than Stairs by Elevators.” Indagatio Didactica 5 (1): 85–102. https://doi.org/10.34624/id.v5i1.4306.
  • Viana, Vera. 2007. “Materiais Didácticos para o Ensino da Geometria Descritiva no Ensino Secundário.” Boletim da Aproged 27.

book chapters

chapters in edited volumes and conference proceedings on geometry, architecture, and their histories.

  • Viana, Vera. 2023. “Non-Uniform Polyhedra Described by Daniele Barbaro.” In Daniele Barbaro and the University of Padova, edited by Kim Williams and Cosimo Monteleone, 109–137. Cham: Springer Nature Switzerland. https://doi.org/10.1007/978-3-031-29483-9_6.
  • Xavier, João Pedro, José Pedro Sousa, Alexandra Castro, and Vera Viana. 2022. “An Introduction to Solid Tessellations with Students of Architecture.” In Polyhedra and Beyond: Selected Contributions from Geometrias’19, Porto, Portugal, September 05–07. Cham: Springer Nature. https://doi.org/10.1007/978-3-030-99116-6_10.
  • Viana, Vera, João Pedro Xavier, Ana Paula Aires, and Helena Campos. 2019. “Interactive Expansion of Achiral Polyhedra.” In Proceedings of the 18th International Conference on Geometry and Graphics (ICGG 2018), 1116–1128. Cham: Springer International Publishing. https://doi.org/10.1007/978-3-319-95588-9_96.
  • Viana, Vera. 2015. “Interactive Resources for an Active Descriptive Geometry Learning.” In Proceedings of the 12th International Conference on Technology in Mathematics Teaching (ICTMT 12), 352–360. Faro: Universidade do Algarve.

didactic books

these textbooks were written for upper‑secondary courses in descriptive geometry and are no longer in print, but they remain part of my didactic work.

  • Viana, Vera. 2013. Duas por Três 10: Geometria Descritiva, 10.º ano: ensino secundário. Portugal: Areal Editores.
  • Viana, Vera. 2014. Duas por Três 11: Geometria Descritiva, 11.º ano: ensino secundário. Portugal: Areal Editores.

edited volumes / proceedings / journal issues

books and special issues I have edited or co‑edited in geometry, drawing, and symmetry studies.

  • Viana, Vera, João Pedro Xavier, and Helena Mena-Matos, eds. 2022. Polyhedra and Beyond. Cham: Springer International Publishing. https://doi.org/10.1007/978-3-030-99116-6.
  • Viana, Vera, Dénes Nagy, and João Pedro Xavier, eds. 2022. Symmetry: Art and Science. 12th SIS–Symmetry Congress [special issue]. Porto: Aproged on behalf of the International Society for the Interdisciplinary Study of Symmetry. https://hdl.handle.net/10216/142586.
  • Viana, Vera, and João Cabeleira, eds. 2021. Jornadas Didácticas 2021: Livro de Resumos. Porto: Aproged.
  • Viana, Vera, Vítor Murtinho, and João Pedro Xavier, eds. 2020. Thinking, Drawing, Modelling. Cham: Springer International Publishing. https://doi.org/10.1007/978-3-030-46804-0.
  • Viana, Vera, ed. 2019. Geometrias’19: Book of Abstracts. Porto: Aproged. https://doi.org/10.24840/978-989-98926-8-2.
  • Cardoso, Vasco, and Vera Viana, eds. 2018. Jornadas Didácticas 2018: Livro de Resumos. Porto: Aproged.
  • Viana, Vera, ed. 2017. Geometrias’17: Book of Abstracts. Porto: Aproged.
  • Viana, Vera, Filipe González, and Gilson Braviano, eds. 2016. Geometrias & Graphica 2015: Proceedings. Porto: Aproged.
  • Viana, Vera, and A. Paio, eds. 2014. Geometrias’14: Proceedings of the XIII APROGED Meeting – New Challenges on Practice, Researching and Teaching Geometries and Drawing. Porto: Aproged.

edited journal issues

conference papers and extended abstracts

written contributions (full papers and extended abstracts) in conference proceedings and books of abstracts.

  • Viana, Vera. Forthcoming. “A Closer Look at 16th‑Century Representations of the Dodecahedron and Related Polyhedra from the Albertina Museum Collection.” Paper accepted for presentation at the 22nd International Conference on Geometry and Graphics, Zagreb, 2026.
  • Viana, Vera. 2025. “The Icosihexahedron Described by Luca Pacioli, Whose Science Will Be Very Useful in Many Aspects, Especially for Those Who Put It to Good Use in Architecture.” Paper presented at Nexus: Relationships Between Architecture and Mathematics, Vicenza, 2025.
  • Viana, Vera. 2024. “Archimedean Solids Known in the Fifteenth and Sixteenth Centuries.” In Book of Abstracts of the 24th Scientific-Professional Colloquium on Geometry and Graphics, Senj, Croatia, 1–5 September 2024. Zagreb: Croatian Society for Geometry and Graphics.
  • Viana, Vera. 2023. “Materializing Daniele Barbaro’s Creativity with 3D Printing.” In Proceedings of Bridges 2023: Mathematics, Art, Music, Architecture, Culture, 313–320. Phoenix: Tessellations Publishing.
  • Viana, Vera. 2022. “Spatial Structures Based on Solid Tessellations.” In Inspiring the Next Generation – Proceedings of the International Conference on Spatial Structures 2020/21 (IASS 2020/21 – Surrey7), edited by Seyed Alireza Behnejad, Gar Parke, and Omidali Samavati, 2159–2170. Surrey: Spatial Structures Research Centre, University of Surrey. https://doi.org/10.15126/900337.
  • Viana, Vera. 2021. “Towards a Systematic Approach of Topological Interlocked Assemblies of Polyhedra.” In Nexus 20/21: Relationships Between Architecture and Mathematics, conference proceedings. Turin: Kim Williams Books.
  • Viana, Vera. 2019. “Tessellations within Tessellations.” In Symmetry: Art and Science – 11th SIS–Symmetry Congress, Kanazawa 2019, conference proceedings. Budapest: International Society for the Interdisciplinary Study of Symmetry.
  • Viana, Vera. 2018. “Interactive Expansion of Achiral Polyhedra.” In The 18th International Conference on Geometry and Graphics, Politecnico di Milano, 3–7 August 2018: 40th Anniversary Book of Abstracts, 215–216. Milan: Politecnico di Milano, on behalf of the International Society for Geometry and Graphics.
  • Viana, Vera. 2018. “Architectonic Tessellations as Constructive Modules.” In Nexus 2018: Architecture and Mathematics, 325–328. Turin: Kim Williams Books.
  • Viana, Vera. 2018. “Topological Interlocking of Convex Regular Polyhedra.” In RCA 2018 – Research Culture in Architecture: International Conference on Cross-Disciplinary Collaboration, conference proceedings. Kaiserslautern: Technische Universität Kaiserslautern..

online resources

web projects

  • Viana, Vera. 2020–. Moving Geometry. Personal research website on the history of science and geometry. https://veraviana.net/.
  • Viana, Vera. 2020–. 2.º site da Aproged. Association website. https://aproged.net/.
  • Viana, Vera. 2010–2020 (currently offline). Geometria Interactiva. Portuguese‑language teaching site.
    • More information about my former website in Portuguese here / Mais informações sobre o meu antigo site em português aqui.
  • Viana, Vera. 2008–. 1.º site da Aproged. Earlier association website. http://aproged.pt/.
  • Viana, Vera. 2007–. Blogue Geometria Descritiva. Blog. https://geometriaveraviana.blogspot.com/.

thesis

doctoral research in science and technology education, focusing on polyhedra and the teaching of geometry.

  • Viana, Vera. 2020. Aplicações didácticas sobre poliedros para o ensino da geometria (Didactic Applications on Polyhedra for the Teaching of Geometry). PhD thesis, Universidade de Trás-os-Montes e Alto Douro. Repositório Científico da UTAD. https://repositorio.utad.pt/handle/10348/10337.

contributions to other authors’ publications

short notes on publications by other authors for which I provided specialised geometric or historical input, formally acknowledged but without co‑authorship

  • Katz, Eugene. “Journey Through Time in the Footsteps of a Polyhedron.” The Mathematical Intelligencer, 2025, https://doi.org/10.1007/s00283-025-10425-x.
    • I provided specialised input on the geometric and historical interpretation of the octagonal bipyramid in Lorenzo Sirigatti’s La Pratica di Prospettiva; this contribution is acknowledged in the article.
  • Foldvari, Grego Gergely. “Tabakgasse‑poliéder” (Tabakgasse polyhedron), 2023. Available at: Facebook post.
    • I provided specialised input on the geometric reconstruction of the base polyhedron; this contribution is acknowledged in the associated publication
  • Williams, Kim. “Daniele Barbaro and the Geometric Solids.” In Daniele Barbaro and the University of Padova, edited by Cosimo Monteleone and Kim Williams, 3–26. Cham: Birkhäuser, 2023. https://doi.org/10.1007/978-3-030-76687-0_1
    • I provided specialised input on the geometric reconstruction and historical interpretation of Barbaro’s polyhedra; this contribution is acknowledged in five footnotes.
  • Leopold, Cornelie. “Geometric and Aesthetic Concepts Based on Pentagonal Structures.” In Handbook of the Mathematics of the Arts and Sciences, edited by Bharath Sriraman, 291–316. Cham: Springer, 2019. https://doi.org/10.1007/978-3-319-70658-0_20-1.
    • I provided specialised scholarly input on the discussion of topologically interlocked assemblies involving the pentagonal dodecahedron and contributed three figures to the chapter; this contribution is acknowledged in the acknowledgements, figure captions, and citations of my research.