NeoTrie VR, New Geometry in Virtual Reality


NeoTrie is a new virtual reality scenario to create, manipulate and play with 3D geometrical objects.

The aim of this project is to design and test some gaming activities in NeoTrie VR (acronym of "Neo" + "Géométrie" + Virtual Reality), a new software package which is currently being developed by Virtual Dor and the University of Almería, that enables pupils to create, manipulate, and interact with 3D geometrical objects and 3D models in general, of several types. It also includes activities and games to solve 3D geometric problems.

The project is addressed to teachers and pupils at primary and secondary schools, as well as universities, interested in educational applications with Virtual Reality. It pays special attention to those aspects of geometry and topology that cause most difficulties for students (or a majority of them) with recent methodologies.

The activities are either for individuals or groups. In the case of groups, collaborative and competitive games are programmed to achieve greater success in the learning process.

The objectives of the project are the following:

  • To examine aspects of plane geometry visible through the eyes of a third dimension.
  • To introduce 3D geometry and modelling meant for 3D printing.
  • To develop handicrafts and 3D visual skills.
  • To stimulate deductive and inductive reasoning skills.
  • To highlight cooperative work and positive interdependence.
  • To motivate pupils by means of recreational, collaborative and competitive games.

The following requirements are made for participants in the project:

Participants in the project can be involved in the processes of the preparation, testing and feedback of the beta versions of NeoTrie VR.

Basic information

Country: Poland, Spain

Coordinator: University of Almería,

Programme: Other

Project Acronym:

Target groups: college students, general public, parents, primary school students, secondary school students, teachers, university students, university lecturers

Topic: Maths, Education

Start year: 2017

End year: 2019


Contact person: José L. Rodríguez, jlrodri (at)

Nowadays, virtual reality provides sensational immersive experiences which are very attractive and motivating, not only for young people but also for adults. Educators’ task is to confirm that this new technology stimulates the acquisition of 3D visual and thinking skills.

NeoTrie VR emerged from the international project "Let's play to classify surfaces!", a project that started in 2016 and combines both manipulative and virtual activities in geometry and topology. This project works on classic graphs problems, knots and links, polyhedral surfaces (generalising tilings and polyhedra, useful in videogames programming or 3D modelling), Euler characteristics, orientability (Moebius band Klein bottle), the genus of a surface, and more.

Pre-tests, tests and post-tests are prepared for the evaluation process, to check the advantages and disadvantages of NeoTrie VR.

The project mainly focuses on the possibilities of virtual reality (VR), which enables pupils to visualise, manipulate and interact with 3D geometric objects. Some manipulative materials (using 3D Polyfelts, ZOME, and others) are also used in the classroom before, during or after the VR experience. As has already been observed in several schools, science fairs and conferences, VR increases interest in 3D geometry and modelling.

The plan is to carry out interactive activities dealing with the following themes. The activities suit students aged 10 to 17, although the project does not distinguish specific ages for using the software, but rather by the level of difficulty.

Among project activities that delve into the basic concepts of plane geometry are:

  • Symmetries, mosaics, planes, parallels and perpendiculars, measures of lengths and angles, recognition of parallelepipeds interacting with them, and playing with lights and shadows.
  • Projections of 3D figures using interactive light bulbs.
  • Construction of several families of polyhedra (Platonics, pyramids, prisms, antiprisms, Archimedean, etc.), and understand some basic operations of polyhedra such as taking duals, truncation, rectification or extension.
  • Generation of curved bodies (sphere, cone, cylinder, torus, etc.) by movements in space.
  • Study of basic properties of polyhedra and metric calculations: Euler characteristics, length, area, volume, etc.
  • Spatial symmetries of 3D figures, generation of crystal structures.
  • Use homotheties and translations to construct some geometric 3D fractals, such as the Sierpinski tetrahedron or the Menger sponge.
  • Generation of crystalline networks from fundamental cells.
  • Graph theory: adapt some classic problems on plane graphs to 3D graphs, such as the Seven Königsberg bridges problem, the Salesman’s problem or the “Four colours theorem”.
  • Other subjects of the curriculum of mathematics suggested by the participants.
  • Applications to other areas of science.


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