<div class="sw-email-modal sw--display-block"> <div id="emailModalContentContainer"> <span class="noty_close sw--position-absolute sw--position-right sw--padding-top-3 sw--padding-right-3 icon-cancel sw--opacity-8"></span> <div class="sw-row"> <div class="sw-email-modal__copy sw--position-relative sw--display-block sw--padding-vert-4"> <p class="last sw--font-size-16">Sign up to get email alerts on discount promotions. There might be one very soon...</p> <form action="/register/email-signup" class="sw-email-modal__signup sw--position-relative" data-confirmation="emailConfirmationModal" data-sw-email-modal-form> <input type="text" class="sw-email-modal__signup-input sw--input-height__medium" placeholder="Email address" name="email" /> <input type="hidden" class="sw-email-modal__signup-input" name="location" value="/product/PCYD8XCGH/clebsch-diagonal-surface-with-numbering?material=27" /> <input type="hidden" class="sw-email-modal__signup-input" name="confirmation" value="emailConfirmationModal" /> <input type="submit" class="btn-primary" value="Sign Up" /> <div id="emailModalFormError" class="text-error" style="display:none"></div> </form> </div> </div> </div>

Click and drag to rotate
[01] Clebsch Diagonal Surface with Numbering 3d printed Description
 [01] Clebsch Diagonal Surface with Numbering 3d printed Description
 [01] Clebsch Diagonal Surface with Numbering 3d printed Description

Not a Photo

[01] Clebsch Diagonal Surface with Numbering

Not For Sale

Product Description

Numbered Clebsch Diagonal Surface (with 27 Lines) [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 while this is the "purest" model, some of the other Clebsch models show objects from the complex Configuration and one prints the imprinted numbers in a color process.
What's in the Box
[01] Clebsch Diagonal Surface with Numbering
15.0 cm
15.0 cm
22.8 cm
Sign In or Join to comment.


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.