When the calculation is complete, the sliced torus is shown with copies of the flattened slices below:
Open Layers on the Window menu and make the various aspects of the model visible.
With the Flat-X slices layer invisible you can see just the Sliceform.
You can also make one of the slice layers invisible, so that you can see the Y slices for example.
Now make just the Flat-X layer visible and go to the Camera menu, choose Standard Views and then Top. Note how some of the slices overlap.
This is easily fixed, the two sets of slices are grouped so just move them so that they are independent.
This is the final step.
The output method you want to use will depend on how you want to produce the physical Sliceform. The following method is the one I use to cut out the slices with scissors.
I used the SVG export plugin from the Ruby Library Depot. There is another one here to give vectors drawings of the slices.
I then loaded the SVG into the vector graphics program Inkscape.
The only problem I found was that the SVG file gives large slices which you have to scale. The SVG has very small font sizes which I increased by edited the SVG file ina text editor. I can add more detail if anyone wants it.
Having scaled the slices, you need to arrange them on the paper in order to cut them out. The slices for each direction need to be on different sheets. You must ensure that both sets are scaled at the same time in order that they fit.
The following posts were originally part of a website called MathsYear2000 which was created that year by the UK Department of Education.
The site was changed to http://www.Counton.org which, because of lack of funding is a shadow of its former sense.
Sliceform models are three-dimensional objects created by slicing a solid many times in two directions. The models are a series of cross sections which are made of a set of planes cut from card slotted together.
Most Sliceforms are continuously deformable from the extremes of two flat shapes which form interesting designs in themselves. The intersections of the slices act as hinges.
The pictures you see here do not show their full beauty. You have to make them and play with their endless shapes and see the way light plays on them as you move them about and deform them. As you move the Sliceforms they change colour dramatically at times. This is apart from the constantly varying and interesting shadows they cast.
Who invented Sliceforms?
The Sliceform technique originated with a mathematician called Olaus Henrici who taught in London at the end of the nineteenth and early twentieth centuries. He made models using cross sections of quartic surfaces; these are similar to a sphere but have with cross sections which are ellipses, hyperbolae or parabolae.
Models were constructed for sale in Germany by the firm of Martin Schilling. These were designed by Alexander von Brill in Darmstadt.
The method for making the models has not been fully exploited, although it has been used for making packing for fruit and other small regular items.
In the nineteenth century mathematical models were made for teaching and understanding geometry. Many museums have collections of these.
The Strange Surfaces exhibition at the Science Museum in London contains Sliceforms from the 19th century to the present day (by Brill and John Sharp) and other interesting historical models of surfaces. Visit their website for more details.
John Sharp has extended the system to a wide range of surfaces and polyhedra, under the name Sliceforms.
See also the post How to make and assemble the models and Sliceform templates and Downloads
The following models are simple ones for you to learn to assemble the models.
In many cases there are more detailed versions or variations which take longer to cut out and assemble because they have more slices.
These models take about ten minutes each to make.
Do not think that because they take such a short time to make that they are any less interesting or complicated to make.
Try them first before you make the more advanced models.
Use them to explore variations with different coloured sets of slices.
Can you make right and left handed versions by colouring?
What types of symmetry do they have?
See also the post on how to make and assemble the models and Sliceform templates and Downloads
The following models are either more advanced versions of the Ten minute Sliceforms or ones with many slices comparable to the ones in John Sharp’s Sliceform book.
These models take about an hour to each to cut out and assemble, depending on how experienced you are.
Even if you have made Sliceforms before, try the Ten minute Sliceforms before you make the more advanced models. In most cases having the simple version to hand will help you when you come to make the more advanced ones.
John Sharp has two books on Sliceforms published by Tarquin.
Sliceforms is a set of eight models to cut out and make.
The models in the book have similar numbers of slices to the advanced models described here. There is a short description of creation of models.
Surfaces: Explorations with Sliceforms
Surfaces is a more advanced book. It describes various techniques for creating Sliceforms from purely artistic methods to mathematical ways of modelling surfaces using this technique.
The Sliceforms Poster is available as thick paper and also in a laminated version.
CLICK ON THE LINKS ABOVE TO GO TO THE TARQUIN SITE TO ORDER THEM