Designing Jigsaw Lamps

Year: 2025 Authors: Rahel Brugger; Oliver Straser; Katja Maaß

Core claim

Jigsaw lamps can be systematically designed from Catalan solids using modular pieces, connection mechanisms, and decoration choices that shape both stability and aesthetics.

Topics

modular lampshade design, symmetry in polyhedra, paper prototyping, decorative styling

Domains

polyhedra, Catalan solids, symmetry, lighting design, paper craft, decorative patterning, product design

Methods

polyhedral analysis, workshop prototyping, Inkscape drafting, plotter cutting

Media

thick paper, polypropylene foil, black pen, laser cutter

Paper text

The text below is the locally extracted OCR/Markdown version of the paper. Raw PDF files remain local and are not published here.

Bridges 2025 Conference Proceedings

Designing Jigsaw Lamps

Rahel Brugger ${}^1$ , Oliver Straser ${}^2$ , and Katja Maaß ${}^3$

International Centre for STEM Education, University of Education Freiburg, Germany ${}^1$ rahel.brugger@ph-freiburg.de, ${}^2$ oliver.straser@ph-freiburg.de, ${}^3$ katja.maass@ph-freiburg.de

Abstract

In the context of a summer school and an open schooling project led by the first author, students and adults designed a range of different symmetrical lampshades that are assembled from many identical pieces. In this article we would like to describe this process, present results and share some insights to enable readers to create their own designs.

What Are Jigsaw Lamps?

By jigsaw lamps we mean spherical lampshades that are assembled from many identical pieces without gluing. The most popular example is the 30-piece “IQlight” (IQ standing for “interlocking quadrilaterals”) by Danish designer Holger Strøm from 1973 [2]. Another beautiful one is the “Vita Lora” lamp by Lorenzo Radaell, made up of 60 parts [5]. Often the shapes of single pieces of jigsaw lamps are quite simple but when they are put together, you get complex-looking lamps with a lot of symmetry that are very aesthetically pleasing.

Figure 1: The commercial lampshade IQlight with its underlying Catalan solid, the rhombic triacontahedron.

Figure 2: The commercial lampshade Vita Lora with its underlying Catalan solid, the deltoidal hexecontahedron.

Brugger, Straser, and Maaß

Underlying Polyhedra

When analyzing lamps like Vita Lora and IQlight mathematically by connecting the points where three or more pieces meet (see Figure 1 and Figure 2), one usually finds a regular polyhedron – in the case of Vita Lora it is the deltoidal hexecontahedron and for IQlight the rhombic triacontahedron. They both belong to the Catalan solids, a class of 13 polyhedra that can be defined via their duals, the Archimedean solids. All Catalan solids are face-transitive, meaning that all faces are congruent and there are symmetries of the entire polyhedron mapping each face to any other. For the jigsaw lamp this means that you only need multiple copies of one single modular piece and the same local construction technique works to connect each of the adjacent faces. Note that there are more polyhedra with this property than the Catalan solids. Under the keyword “isohedra” you can find the full list with some very nice-looking “distorted” Platonic or Catalan solids as other examples.

However, as the Catalan solids already provide a good variety of polyhedra with a suitable degree of complexity, we restricted ourselves to them in our workshops. Most participants found that the solids with rhombuses, kites or pentagons as faces gave more aesthetically pleasing results than the ones with triangles, maybe because in these cases the shape of the polyhedron was usually less visually present in the final result. The lamps in Figure 3 are both based on the pentagonal hexecontahedron, a Catalan solid we have not seen in commercial designs so far.

(a)

(b)

Figure 3: A space-themed (a) and a seaside-themed (b) jigsaw lamp, both based on the pentagonal hexecontahedron (see Figure 4(b)).

The lamp in Figure 3(a) deviates slightly from our design principle that all pieces should look the same. In this case we have two different pieces (30 of each) that only differ at one edge where always two different pieces meet. In fact, this even breaks most of the lamp’s symmetry (no matter how you distribute the tails of the shooting stars, you can only keep one axis of rotational symmetry). Of course, one could soften our definition of jigsaw lamps even further and use polyhedra with non-congruent faces, such as Archimedean solids. We have not seen this in commercial designs or tried it out (the result might be visually quite chaotic if the design is not kept very simple) but we encourage the reader to do so.

It sometimes has turned out necessary that the angles in the lamp piece differ a bit from the angles that you can look up for the polyhedron’s faces. This probably has to do with the fact that paper bends. You will find this out when prototyping your lampshade. If a vertex is too sharp, the adjacent angles in the lamp piece must be increased, if the vertex is too flat, the angles must be reduced.

Designing Jigsaw Lamps

How to Connect the Faces

However, there is more to a jigsaw lamp than the underlying solid. Most importantly, you need to find a way to connect the pieces. There are different ways to do this.

Hooks on vertices of the faces might be the most common way, for example used in IQlight. Where the hooks meet, you get nice rosette patterns that can be styled in different ways, see for example Figure 6. You can also find hooks in Figure 3(a) at the vertices where little circles are formed (in the picture the lamp is assembled in a way that they are inside and only become visible when the light is turned on) and in Figure 3(b) at the whirls and the starfish.

Jigsaw-like connections on edges like in Vita Lora need a bulge on one edge and a suitable place to insert it where it meets the other edge. This can either be created by the shape of the edge as with the fish fins in Figure 3(b) and with Vita Lora (in fact, for Vita Lora, only this mechanism holds the pieces together—the threefold and fivefold rosettes look very similar to hooks but do not contribute to the stability of the lamp). Or you use something similar to a “tabs and slots” mechanism or “mortise-and-tenon-joints” [4] known from wood or metal work. Note that the paper bulges, having less friction and more flexibility, should only just fit through the slit by bending the paper so that it does not slip back. You can see this in Figure 5 where the mole is coming out of the hill and in many designs from the online shop MYOL [3].

Slide-together connections on edges, as far as we know, are not common in commercial jigsaw lamps, maybe because they give less stability or because you automatically get straight lines in your design. But they are often used in other contexts (see [1] and [4]) and our participants liked them. You find them in Figure 3(a) at the small and the big stars, in Figure 3(b) at the shell and in Figure 5 at the hills that have no mole coming out.

Before designing the connections, it is important to realize which vertices and edges meet. This is particularly interesting for the two polyhedra in Figure 4, which were very popular among our participants. Unlike the other Catalan solids, they have vertices with no symmetry axis passing through (which is why different vertices of the lamp piece meet there) and symmetry axes through the centers of edges (which is why this edge meets “itself”). Our participants found it helpful to first draw a diagram as in (c), which is valid for both solids (with in one case four and in the other case five copies of the lower vertex meeting).

(a)

(b)

(c)

Figure 4: The pentagonal icositetrahedron (a) and the pentagonal hexecontahedron (b). Note that both polyhedra have second versions where everything is mirrored.

Figure 5: A mole-themed jigsaw lamp based on the deltoidal icositetrahedron.

Brugger, Straser, and Maaß

Decorations

Two lamps with the same underlying polyhedron and the same way to connect the faces can still be styled very differently as you can see in Figure 6.

(a)

Figure 6: Floral variations of IQlight designed (a) by students from Marie-Curie-Gymnasium Kirchzarten and (b) by Inga Langguth at CdE Summer Academy.

(b)

Incorporating large decorative elements may complicate assembly, which was the case for the lamp in Figure 6(b). It is also sometimes difficult to predict which parts will overlap when the pieces are put together or exactly what effects will be created by several layers of paper on top of each other when you turn on the lights. The easiest way to find out is to try.

Practical Implementation

Except for IQlight and Vita Lora, all the lamps shown here were designed by the participants of a one-week summer school, by eighth and ninth graders on two mornings as part of an open schooling project or by the first author. We used a plotter that can scan a single piece (drawn with a black pen or cut from black paper) or designed the pieces directly in Inkscape. Then we cut many copies of it from thick paper $(150-300\mathrm{g}/{\mathrm{m}}^2)$ with the plotter. Cutting such pieces by hand is very time-consuming but can of course be done in small amounts for first tests. Several iterations of prototyping were necessary to achieve the final versions. It is also possible to use a laser cutter to make weather resistant plastic versions of the lamps. For this, we used $0.3\mathrm{mm}$ polypropylene foil, which was sold as cover sheets.

Acknowledgements

We thank our participants at CdE Summer Academy 2024 and the open schooling project at the math club of Marie-Curie-Gymnasium Kirchzarten for finding all of this out together with us. The open schooling project was carried out within ICSE Science Factory which is funded by the European Union.

References

[1] G. W. Hart. “Slide-Together’ Geometric Paper Constructions.” Bridges for Teachers, Teachers for Bridges, 2004 Workshop Book, Winfield, USA, Jul. 30 – Aug. 1, 2004, pp. 31-42. https://www.georgehart.com/slide-togethers/slide-togethers. [2] IQlight. https://www.iqlight.com [3] MYOL. https://www.make-your-own-lamp.de/produkt-kategorie/diy-bausaetze/neue-puzzle-teile/ [4] R. Roelofs. “Slide-Together Structures.” Bridges Conference Proceedings, London, UK, Aug. 4-8, 2006, pp. 161-170. https://archive.bridgesmathart.org/2006/bridges2006-161.pdf [5] Vita Lora. https://umage.de/products/lora