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

Educational and online resources | as author and co-author | seminars, workshops, etc. | oral presentations | as editor and co-editor | events and committees

journal articles

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

  • Viana, Vera. Forthcoming. “Luca Pacioli’s Vigintisex Basium Planum (Rhombicuboctahedron): Description, Construction, and Architectural Reception.” Nexus Network Journal.
  • 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

didactic books for teaching descriptive geometry at secondary level.

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

edited volumes / proceedings

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: International Society for the Interdisciplinary Study of Symmetry and the local organizing committee. 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.

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 to be presented 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.
  • Castro, Alexandra, Vera Viana, João Pedro Xavier, and José Pedro Sousa. 2019. “An Introduction to Solid Tessellations with Students of Architecture.” In Polyhedra and Beyond: Selected Contributions from Geometrias’19, Porto, Portugal, September 05–07, 137–147. Cham: Springer Nature. https://doi.org/10.1007/978-3-030-99116-6_10.
  • 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. [Title to be added]. In [Title of the book of abstracts associated with re.public.polimi.it handle 11311/1072192], [page range to be added]. Milan: Politecnico di Milano.
  • 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..

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.

SEMINAR / WORKSHOPS / COURSES / DISCIPLINES TAUGHT

  • Six lectures on Preenchimento do Espaço com Poliedros included in the syllabus “Geometry and Architecture” for 1st year students @ Faculty of Architecture, University of Porto, Portugal, | March-April, 2017
  • Descriptive Geometry classes at Portuguese Secondary Schools | 1994 to 2011
  • Continuing Training Course Produção de Materiais Didácticos para o Ensino da Geometria com o apoio das TIC @ ISCTE – nstituto Universitário de Lisboa, Portugal | 2010
  • Continuing Training Course Produção de Materiais Didácticos para o Ensino da Geometria com o apoio das TIC @ Colégio de Santa Doroteia, Lisboa, Portugal | 2009

ORAL PRESENTATIONS

  1. 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 with oral presentation included in the Nexus 2025 Relationships between Architecture and Mathematics | 3-6 June 2025 | Vicenza, Italy
  2. Dos Cubos e Octaedros e seus derivados ao Facetamento e Estrelação de Poliedros. Invited lecture for students pursuing a master’s degree in mathematics Education @ Faculty of Sciences of the University of Porto | 19 May 2025
  3. Dos Cubos e Octaedros e seus derivados ao Facetamento e Estrelação de Poliedros. Invited lecture for undergraduate students pursuing a degree in Drawing @ Faculty of Fine Arts of the University of Porto | 02 May 2025
  4. Archimedean Solids known in the Fifteenth and Sixteenth Centuries. Plenary session as keynote speaker, included in the 24th Scientific-Professional Colloquium on Geometry and Graphics | 1–5 September 2024 | Senj, Croatia
  5. Materializing Daniele Barbaro’s Creativity with 3D Printing. Regular paper with oral presentation included in the Bridges Halifax 2023 | July 2023 | Dalhousie University, Canada.
  6. Studying Polyhedra with Advanced Digital Tools. Invited lecture included in the Art and Math Seminar Spring 2022, organised by the Department of Mathematics at Kansas State University, United States of America | 21. April 2022
  7. Spatial Structures Based on Solid Tessellations. Paper with oral presentation included in the IASS Annual Symposium and Spatial Structures Conference | August 2021, University of Surrey, England.
  8. Towards a Systematic Approach of Topological Interlocked Assemblies of Polyhedra. Paper with oral presentation included in the Nexus 20/21: Relationships Between Architecture and Mathematics | September 2021, Faculty of Architecture, TU Kaiserslautern, Germany.
  9. Tessellating and Interlocking in Patterns. Invited lecture included in the Summer Semester “Pattern Matters” in the Faculty of Architektur Technische Universität Kaiserslautern, Germany | 18 May 2021
  10. Non-uniform Polyhedra in Barbaro’s La Pratica della Perspettiva. Invited lecture included in the Giornata di studi – Daniele Barbaro e lo Studio Patavino | December 2020, Universitá di Padova, Italy.
  11. Tessellations Within Tessellations. Paper with oral presentation included in the Symmetry Art and Science: 11th Congress and Exhibition | November 2019, Kanazawa Institute of Technology, Japan.
  12. Geometria Descritiva Interactiva. Keynote lecture included in the 2º Workshop – Software Livre de Matemática | July 2019, Instituto Superior de Engenharia de Coimbra, Portugal.
  13. Preenchimento Uniforme do Espaço com Poliedros Convexos. Invited lecture included in the syllabus “Discursos Interdisciplinares sobre Geometria” @ Faculty of Fine Arts, University of Porto, Portugal | 2018
  14. Topological Interlocking of Convex Regular Polyhedra. Poster with oral presentation included in the RCA 2018: Research Culture in Architecture. International Conference on Cross-Disciplinary Collaboration | September 2018, Faculty of Architecture, TU Kaiserslautern, Germany.
  15. Interactive Expansion of Achiral Polyhedra. Paper with oral presentation included in the ICGG18: 18th International Conference on Geometry and Graphics | August 2018, Politecnico di Milano, Italy.
  16. Architectonic Tessellations as Constructive Modules. Poster with oral presentation included in the Nexus 2018: Relationships between Architecture and Mathematics |  July 2018, Università di Pisa, Italy.
  17. Axonometric Representations in Solid Geometry Teaching. Poster presentation included in the Nexus 2016: Relationships between Architecture and Mathematics | July 2016, Biblioteca Campus de Gipuzkoa Donostia, San-Sebastian, Spain.
  18. Interactive Resources for an Active Descriptive Geometry Learning. Paper presentation included in the 12th International Conference on Technology in Mathematics Teaching | July 2015, Faculdade de Ciências e Tecnologia da Universidade do Algarve, Portugal.
  19. Recursos digitais para a Didática e a Aprendizagem da Geometria Descritiva. Keynote lecture included in the Projeto TEA – Tablets no Ensino e na Aprendizagem – Fundação Calouste Gulbenkian | January 2015, Escola Secundária Eça de Queirós, Lisboa, Portugal.
  20. Dynamic Geometry Software and Augmented Reality Samples for High School Descriptive Geometry Teaching. Paper with oral presentation included in the Enabling Teachers for Entrepreneurship Education |  June 2014, Universidad de Granada, Spain.
  21. Construções Dinâmicas com o Geogebra. Workshop included in ProfMat 2014 Braga, Portugal  | 2014
  22. Descriptive Geometry Learning Is No More Threatened by Dynamic Geometry Software Than Stairs by Elevators. Paper with oral presentation included in the III Dia Geogebra em Portugal | June 2013, Universidade de Aveiro, Portugal.
  23. Introdução ao Rhinoceros. Workshop included in the Geometrias’13 Conference | June, Faculty of Architecture, University of Porto, Portugal
  24. Construção de exercícios interactivos com o C.a.R. Metal e o Geogebra. Workshop included in the XII Encontro Regional da Aproged, Vila Real, Portugal | 2012

AS EDITOR AND CO-EDITOR

EVENTS AND COMMITTEES:

  • SCIENTIFIC/PROGRAM COMMITTEE MEMBER (reviewer):
    1. 2026: Bridges 2026 (upcoming)
    2. 2026: ICGG 2026 (upcoming)
    3. 2025: Bridges 2025
    4. 2025: Nexus Conference 2025
    5. 2024: Bridges 2024
    6. 2024: ICGG 2024
    7. 2023: Bridges 2023
    8. 2023: CAAD Futures 2023 (sub-reviewer)
    9. 2023: Mongeometrija 2023
    10. 2022: ICGG 2022
    11. 2022: Bridges 2022
    12. 2022: 12th SIS-Symmetry Congress 2022
    13. 2021: IS4SI 2021
    14. 2021: Nexus Conference 20/21
    15. 2020: ICGG 2020
    16. 2019: Geometrias’19
    17. 2018: ICGG 2018
    18. 2018: Mongeometrija 2018
    19. 2015: ICTMT 12 (sub-reviewer)

  • ASSOCIATION MEMBER:
    • NEXUS: Relationships between Architecture and Mathematics, since 05.2025
    • SIS-Symmetry: International Society for the Interdisciplinary Study of Symmetry, since 11.2019
    • ISGG: International Society for Geometry and Graphics, since 08.2018
    • APROGED: Portuguese Geometry and Drawing Teachers Association, since 01.1999