Pair-of-pants surface

by dennedesigns, published

Pair-of-pants surface by dennedesigns Feb 1, 2016
2 Share
Download All Files

Thing Apps Enabled

Order This Printed View All Apps

Design Tools


Liked By

View All

Give a Shout Out

If you print this Thing and display it in public proudly give attribution by printing and displaying this tag.

Print Thing Tag


Thing Statistics

530Views 439Downloads Found in Math


Here is a pair-of-pants surface designed for the InforMath project funded by the National Science Foundation (DRL-1323587). The InforMath project (http://informalmathematics.org/) is a partnership between San Diego State University and several museums at the Balboa Park, including the Reuben H. Fleet Science Center (http://www.rhfleet.org/)

These models are designed to join together using small magnets. There are two options for the print files, ones with small holes for the magnets and ones without. There is a ring system too, so that you have more flexibility in how the models are put together. There are also thin versions of the models (with no magnet holes).

More information about the models, including how they were designed can be found at http://mathvis.academic.wlu.edu/2016/02/09/constructing-a-pair-of-pants/ and http://mathvis.academic.wlu.edu/2016/02/09/pair-of-pants-surfaces-the-math/.

Print Settings

Printer Brand:












The models are sized to fit in your hand. You may have to scale by a factor of 10 if you're using MakerWare, since it tends to import files in mm, not cm.

I printed without a raft, but with extra strong supports. The standard supports tended to be knocked around by the printer nozzle. Under Print Settings, go to Custom, then Supports and Bridging. Check the Supports box, then uncheck the Align Supports box.


The pair-of-pants, caps, etc are held together by 3mm (diameter) x 3mm (height) cylindrical rare earth magnets (http://www.gaussboys.com/store/index.php/magnet-shapes/cylinders/c0303.html).

The magnets should fit snugly, and I didn't need any glue. If you do, you could try using a little JB Weld epoxy just in case. I suspect that you could also use superglue. I highly recommend printing DesignByNumber's magnet insertion tools (http://www.thingiverse.com/thing:436565) to help seat the magnets into the little holes.

For the pair-of-pants and caps models, I alternated the + and – ends of magnets around the rims of the pair-of-pants. I did this in a consistent way, for example the + was always at the front and back of the pants. For the rings, the plain ones should be aligned the same alternating way on the top and bottom rims. The ones with plus/minus signs or 90 degrees should have the arrangement rotated by 90 degrees.

The Rueben H. Fleet Science Museum in San Diego made the body of the regular and bent pair of pants be +, then made all the rings -. Not sure what they did with the caps, probably made them all + too. This keeps it very simple.

How I Designed This

A complete description can be found on my blog at http://mathvis.academic.wlu.edu/2016/02/09/constructing-a-pair-of-pants/

A very brief description of the mathematics can be found here: http://mathvis.academic.wlu.edu/2016/02/09/pair-of-pants-surfaces-the-math/

More from Math

view more

All Apps

Auto-magically prepare your 3D models for 3D printing. A cloud based 3D models Preparing and Healing solution for 3D Printing, MakePrintable provides features for model repairing, wall thickness...

App Info Launch App

Kiri:Moto is an integrated cloud-based slicer and tool-path generator for 3D Printing, CAM / CNC and Laser cutting. *** 3D printing mode provides model slicing and GCode output using built-in...

App Info Launch App
KiriMoto Thing App

With 3D Slash, you can edit 3d models like a stonecutter. A unique interface: as fun as a building game! The perfect tool for non-designers and children to create in 3D.

App Info Launch App

Print through a distributed network of 3D printing enthusiasts from across the US, at a fraction of the cost of the competitors. We want to change the world for the better through technology, an...

App Info Launch App

Quickly Scale, Mirror or Cut your 3D Models

App Info Launch App

Treatstock is an online platform that offers decentralized manufacturing services such as 3D printing and CNC machining for clients all over the world. We offer free and instant access to comparati...

App Info Launch App

3D print your favourite design with NinjaPrototype, a professional 3D manufacture with consistent quality and speed.

App Info Launch App

Thank you. I created them to illustrate a concept from topology: Any orientable surface of genus at least 2 may be decomposed into a sum of pairs of pants. Check out https://en.wikipedia.org/wiki/Pair_of_pants_(mathematics). These models were printed and displayed in the Fleet Science Center in San Diego, as part of the (now closed) Taping Shape exhibit there.

Its a pretty neat shape. In fact, somehow it seems that it should prove very useful in some context, but I'm not sure what. Its just a gut feeling. They're not exactly "The Wrong Trousers" :-) I would have been tempted to build this using OpenScad, boolean adding together a bunch of 30 degree torus sections and then boolean subtracting out paths similarly. The shape would not be quite the same. Nothing would be squarish, which may have been desirable here. It would be fun to make the legs half the size and generate an n level fractal with poly-trousers with 4, 8, 16, 32.... leg holes. Again, I'm not sure what one would do with such a manifold, but something may come to mind to someone. :-) Perhaps it would be enough for it to be fun to look at. Not everything has to have a utilitarian purpose. :-)