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8-13 June 2017: 3D Printing Workshop

This event took place in Durham and was funded by Durham University. It was organised by Herbert Gangl (Durham Maths), Ioannis Ivrissimtzis (Durham CS), and Norbert Peyerimhoff (Durham Maths), and was a training opportunity for our students. Confirmed presenters were Bekrokh Eskandari (Peacocks Orthotics Limited, Newcastle), Sabetta Matsumoto (Georgia Tech), Saul Schleimer (Warwick), and Henry Segerman (Oklahoma State). All talks were open for the public and took place in the rooms CG91, CG93, CM105 and CM107. Many thanks to Michael Armstrong and Jason Anderson (both Durham Physics) for having provided us with their Ultimaker 2+ which ran without a hitch during the workshop.


Thursday, 8 June “Mathematical Visualisation Day”

  • 13.00-14.00 Workshop talk by Saul Schleimer (CG91): Symmetries and the Klein quartic
  • 14.00-14.30 Tea/Coffee break, Scarborough Dining Hall
  • 14.30-15.00 Activity (CM103): My first 3D model
  • 15.00-16.00 Talk by Ioannis Ivrissimtzis (CM107): Introduction to 3D modelling
  • 16.00-17.00 Design and Modelling Activities (CM103)
  • 17.00-18.00 PUBLIC LECTURE by Henry Segerman (CG93): 3D Shadows: Casting light on the fourth dimension (see poster)

Friday, 9 June “Research and Applications Day”

  • 10.00-11.00 Workshop talk by Sabetta Matsumoto (CG91): Programmable Matter: using 3D printed elastic instabilities to direct shape transformation
  • 11.00-11.30 Tea/Coffee break, Scarborough Dining Hall
  • 11.30-12.30 Workshop talk by Behrokh Eskandari (CG91): 3D printing in orthotic devices within the health care industry
  • 12.30-13.30 Lunch, Scarborough Dining Hall
  • 13.30-14.30 Design and Printing Activities (CM103)
  • 14.30-15.30 Colloquium style talk by Henry Segerman (CG91): Design of 3D printed mathematical art
  • 15.30-16.00 Tea/Coffee break, Scarborough Dining Hall
  • 16.00-17.00 Design and Printing Activities (CM103)

Monday, 12 June “Active Engagement Day”

  • 10.00-10.30 Presentation (CG91) by David Hoyle (Maths, Durham) on analysing molecular architecture of 3D printing materials
  • 10.30-12.30 Short presentations (CG91) on 3D printing projects on Durham Campus: Margarita Staykova (Physics, 10.30-11.00), Catriona Sellick (Earth Sciences, 11.30-12.00), Michael Cooke (Engineering and Computer Science, 12.00-12.30)
  • 11.00-11.30 Tea/Coffee break, Scarborough Dining Hall
  • 12.30-13.00 Presentation (CG91) by Quoc Vuong (Neuroscience, Newcastle) on experimental work in cognitive psychology using 3D printed familiar and novel objects
  • 13.00-13.30 Lunch, Scarborough Dining Hall
  • 13.30-15.00 Design and Printing Activities (CM103)
  • 15.00-15.30 Tea/Coffee break (CM103)
  • 15.30-16.00 Design and Printing Activities(CM103)
  • 16.00-16.30 Presentation of the Powderbed ZPrinter 650 (Beth Upex) and Lulzbot Taz6 Printer (Catriona Sellick) at the Archaeology Department, Durham
  • 16.30-17.00 Design and Printing Activities(CM103)

The workshop time between talks on Thursday, Friday, and Monday was filled by hands on activities on design, coding, and printing of models. We also booked the computer rooms CM001 and CM002 for all day Thursday, Friday, and Monday.

Tuesday, 13 June “3D-Lab Excursion Day”

Workshop participants had a creative day out and visit FabLab in Sunderland. Participants from Durham were picked up by bus at the Security Barrier at 9.15am and at 15.30 from FabLab. Participants from Newcastle got to Sunderland by using the Metro (Green Line). Buffet Lunch was be provided there. Rough outline of schedule:

  • 10.00-10.30 Arrive, tour of the space and introduction to FabLabs and digital fabrication equipment
  • 10.30-11.15 3D printing technologies, history and future
  • 11.15-11.30 SHORT BREAK
  • 11.30-12.15 3D modelling techniques (demonstration):
    • Online sources
    • CAD modelling (Fusion360)
    • Working with scan data (clean up tools: MeshMixer, MeshLab)
  • 12.15-12.45 LUNCH
  • 12.45-13.30 3D modelling techniques (demonstration):
    • Slicing (Cura) and running 3D prints
  • 13.30-15.00 Practical sessions (three concurrent options):
    • Scanning for busts
    • Try CAD modelling (Fusion360)
    • Intro to laser cutting (make a keyring)
  • 15.00-15.15 Closing discussion and Q&A

Sabetta, Saul, and Henry are also organizers of

Brilliant Geometry

an interactive exhibition on the art of mathematical projections. Details about this exhibitions:

11.00-18.00, Friday, 12th May – Sunday, 4th June 2017 at the Summerhall Gallery : 1 Summerhall, Edinburgh EH9 1PL.

Saul Schleimer (Warwick, Maths): Symmetries and the Klein quartic

Abstract (joint work with Henry Segerman): Mathematics has been called the science of patterns.  Some of the oldest, most symmetric, and most beautiful patterns are the tilings of the sphere and of the plane.  As examples, we consider the facets of a jewel or the cells of the bees’ honeycomb.  Mathematicians have generalised these tilings to the hyperbolic plane; one of the most famous illustrations of these are MC Escher’s “Circle Limit” prints.

Tilings of the sphere are always finite.  Tilings of the plane and of the hyperbolic plane are necessarily infinite – they require an unbounded number of tiles.  Since infinity is a difficult idea to understand or to use, we search for ways to “wrap-up” the tilings into a finite, bounded object.  For frieze patterns this idea dates back to antiquity.  Wrapping up the plane is more subtle; wrapping up the hyperbolic plane is still an area of active research! We’ll illustrate all of these ideas with several examples; the last of these will be wrapping the (2,3,7) triangle tiling of the hyperbolic plane around Felix Klein’s famous quartic curve.

Public Talk by Henry Segerman (Oklahoma State University, Maths): 3D Shadows: Casting light on the fourth dimension

Abstract: Our brains have evolved in a three-dimensional environment, and so we are very good at visualising two- and three-dimensional objects. But what about four-dimensional objects? The best we can really do is to look at three-dimensional “shadows”. Just as a shadow of a three-dimensional object squishes it into the two-dimensional plane, we can squish a four-dimensional shape into three-dimensional space, where we can then make a sculpture of it. If the four-dimensional object isn’t too complicated and we choose a good way to squish it, then we can get a very good sense of what it is like. We will explore the sphere in four-dimensional space, the four-dimensional polytopes (which are the four-dimensional versions of the three-dimensional polyhedra), and various 3D printed sculptures, puzzles, and virtual reality experiences that have come from thinking about these things. I talk about these topics and much more in my new book, “Visualizing Mathematics with 3D Printing”.

Here is a short video of Henry Segerman on youtube!

Henry Segerman (Oklahoma State University, Maths): Design of 3D printed mathematical art

Abstract: When visualising topological objects via 3D printing, we need a three-dimensional geometric representation of the object. There are approximately three broad strategies for doing this: “Manual” – using whatever design software is available to build the object by hand; “Parametric/Implicit” – generating the desired geometry using a parametrisation or implicit description of the object; and “Iterative” – numerically solving an optimisation problem.

The manual strategy is unlikely to produce good results unless the subject is very simple. In general, if there is a reasonably canonical geometric structure on the topological object, then we hope to be able to produce a parametrisation of it. However, in many cases this seems to be impossible and some form of iterative method is the best we can do. Within the parametric setting, there are still better and worse ways to proceed. For example, a geometric representation should demonstrate as many of the symmetries of the object as possible. There are similar issues in making three-dimensional representations of higher dimensional objects. I will discuss these matters with many examples, including visualisation of four-dimensional polytopes (using orthogonal versus stereographic projection) and Seifert surfaces (comparing my work with Saul Schleimer with Jack van Wijk’s iterative techniques).

I will also describe some computational problems that have come up in my 3D printed work, including the design of 3D printed mobiles (joint work with Marco Mahler), “Triple gear” and a visualisation of the Klein Quartic (joint work with Saul Schleimer), and hinged surfaces with negative curvature (joint work with Geoffrey Irving).

Sabetta Matsumoto (Georgia Tech, Physics): Programmable Matter: using 3D printed elastic instabilities to direct shape transformation

Abstract: 3D printed programmable matter has the potential to revolutionize manufacturing in fields ranging from organs-on-a-chip to architecture to soft robotics. By expanding the pallet of 3D printable materials to include the use stimuli responsive inks, this nascent 3D printing technique promises precise control over patterned shape transformations. With the goal of creating a new manufacturing technique, we have recently introduced a biomimetic printing platform that enables the direct control of local anisotropy into both the elastic moduli and the swelling response of the ink.

We have drawn inspiration from nastic plant movements to design a phytomimetic ink and printing process that enables patterned dynamic shape change upon exposure to water, and possibly other external stimuli. Our novel fiber-reinforced hydrogel ink enables local control over anisotropies not only in the elastic moduli, but more importantly in the swelling. Upon hydration, the hydrogel changes shape according the arbitrarily complex microstructure imparted during the printing process. 

To use this process as a design tool, we must solve the inverse problem of prescribing the pattern of anisotropies required to generate a given curved target structure. We show how to do this by constructing a theory of anisotropic plates and shells that can respond to local metric changes induced by anisotropic swelling. A series of experiments corroborate our model by producing a range of target shapes inspired by the morphological diversity of flower petals.

Behrokh Eskandari (Peacocks Orthotics Limited, Newcastle): 3D printing in orthotic devices within the health care industry

Orthoses are externally applied devices used to modify the structural and functional characteristics of the neuromuscular and skeletal system by supporting the body, realigning it or redistributing pressure in a joint or body segment. A big segment of the orthotic market is the custom-made devices. These devices are completely bespoke and customised for individual patient.

The current manufacturing process is labour intensive and manual. Additionally the lack of repeatability and consistency in the manufacturing process results in rework which is a huge burden on national and private health sectors.

Additive manufacturing has been getting a significant amount of interest in recent years. Working with AM on daily basis has proved that this is not answer to all. However it has proven to be a suitable and beneficial process to create such complex and unique products such as orthotic devices. This presentation will show a brief overview of the orthotic industry, current processes as well as pros and cons of AM and how it changes the future of this industry.

Photos from the workshop

Photos of speakers

Henry Segerman and various 3D Printed models

Sabetta, Henry, and Saul presenting proudly models of the Klein Quartic

Sabetta Matsumoto’s talk on 3D printed programmable matter

Becky Eskandari’s talk on 3D printing of orthotic devices

David Hoyle presenting research on the molecular architecture of 3D printing materials

Margarita Staykova’s talk “3D Printing of soft and biological matter”

Catriona Sellick’s talk “From Digital Rocks to Physical Objects”

Michael Cooke’s talk “Additive Manufacture”

Quoc Vuong presenting experimental work in cognitive psychology
using 3D printed familiar and novel objects

Various 3D printers and one laser cutter (can you find it?)

Design and modelling activities

Samples of our 3D printed models

Visit of the Archaeology Lab

Excursion Day at FabLab, Sunderland