[01] Colored and Numbered Clebsch Diagonal Surface

by universaljointNU Visit Shop

  • 3D printed just for you.
  • [01] Colored and Numbered Clebsch Diagonal Surface:


Not For Sale

About this Product

Clebsch Diagonal Surface with Color [01].

The Clebsch Diagonal Surface is a non-singular (i.e. smooth) Cubic Surface originally discovered and documented by Alfred Clebsch (1833 - 1872). The Clebsch Diagonal is a historically important model and was of great interest to early machine designers and mathematicians.

This model is a recreation of the original plaster model made by hand in the 1800's under the direction of Felix Klein. This is a FULL SIZE 1:1 version.

It shows the 27 possible lines on a smooth cubic surface and is the "god-head" of the series of 23 types of singularities possible on a Cubic Surface (that are also shown on Shapeways).

All the lines are numbered with imprinted numbering of the complex configuration. In total there are 36 possible ways to number the lines.

This series of Clebsch models show various aspects of the complex configuration of geometric objects on this famous surface. Please see the model description to make sure which model contains which objects in the configuration. We'd also be happy to customize a model for you.

The Configuration: 27 total lines: 15 Diagonal Lines and 12 Horizontal Lines (Shafli's "Double Six") 30 points where 2 lines of ruling intersect 24 within the model and 6 at infinity 10 points where 3 lines of ruling intersect (Eckardt Points)
- 7 within the model and 3 at infinity The Sylvester Pentahedron Additionally there are three "passages" which can be seen in the animation below. Three are "holes" that can be easily seen. Three are within the model at the "ears" and the seventh is somewhat vertical at the "waist".

http://formpig.com/blog/?p=3253 http://formpig.com/blog/?p=3311 http://formpig.com/blog/?p=2893

For additional documentation or other models or sizes please contact the author. Note that this models is the same as the Clebsch Diagonal Surface with Imprinted Numbers - with the addition of the numbers being produced in /color/ via a colored rapid prototyping process.
What's in the Box

[01] Colored and Numbered Clebsch Diagonal Surface in Transparent Acrylic
Width Height Depth
0 cm 0 cm 0 cm
This model is 3D Printed in Transparent Acrylic: Firm translucent plastic with a smooth surface and rubbery feel.
Model version 1 | Last updated on 01/28/2015

Sign In or Join to comment.
  • 3D printed just for you.
  • [01] Colored and Numbered Clebsch Diagonal Surface:


Not For Sale


We're sorry to inform you that we no longer support this browser and can't confirm that everything will work as expected. For the best Shapeways experience, please use one of the following browsers:

Click anywhere outside this window to continue.