<div id="cookie_notice" class="sw-row sw--padding-2 sw--padding-bottom-1-force sw--text-center sw--bg-grey" > <div class="col-1-2 col-1-1--tab col--no-padding sw--display-inline-block sw--float-none sw--text-left sw--vertical-align__middle"> <p class="col-1-2 col--no-padding small">We use cookies to offer you a better browsing experience. By continuing to use the site you agree to their use. You can find out more about our cookies and read our privacy policy <a href="/legal/privacy-statement" target="_blank">here.</a></p> <div class="col-1-2 col--no-padding sw--text-center"> <div class="col-1-2 col--no-padding sw--display-inline-block sw--float-none"> <a class="sw-dms-button noty_close col-1-1 col--no-padding" data-sw-set-cookie="euCookie">OK</a> </div> </div> </div> </div>

<div class="sw--display-block sw--text-white" style="background-color: #1e2740"> <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 sw--z-index-10"></span> <div class="sw-row"> <div class="sw--position-relative sw--display-block sw--padding-3" style="min-width: 380px"> <p class="sw--font-size-16 sw--margin-bottom-2 sw--margin-right-6">Sign up to hear about special promotions</p> <form action="/register/email-signup" class="sw--position-relative" data-confirmation="emailConfirmationModal" data-sw-email-modal-form> <input type="text" class="sw--input-height__medium" style="width:60%;" placeholder="Email address" name="email" /> <input type="hidden" class="" name="location" value="/product/R5ZGQ27UY/xyz-projective-plane" /> <input type="hidden" class="" name="confirmation" value="emailConfirmationModal" /> <input type="submit" class="btn-primary sw--margin-left-1" value="Subscribe" /> <div id="emailModalFormError" class="text-error" style="display:none"></div> </form> </div> </div> </div>

Click and drag to rotate
xyz Projective Plane 3d printed

Not a Photo

Yellow Processed Versatile Plastic
xyz Projective Plane 3d printed
xyz Projective Plane 3d printed

Not a Photo

xyz Projective Plane

3D printed in deep yellow, richly colored nylon plastic with a smooth finish.
Product Description
This is an xyz drawing of a graph representing the Real Projective Plane.  Notice that there are 12+4=16 balls representing vertices and 12+12=24 struts representing edges.  12 of the struts lie in the facial planes of a cube, coming in 6 pairs, each forming a false intersection at the center of a corresponding face of the cube.  It is called an "xyz drawing" because every edge is parallel to one of the three coordinate axes.

One should also imagine that there are 3+6 faces.  To be more specific, there are 3 square faces and 6 self-intersecting hexagons.  The squares are easiest to identify; each is comprised of 4 balls and 4 struts and the three of them are mutually perpendicular, lying in three planes of symmetry of the cube.  Each of the six hexagons, comprised of 6 balls and 6 struts, lies in a face of the cube and is self-intersecting.

Collecting these data, notice that the Euler characteristic of this is v-e+f=16-24+9=1.  The only compact 2-dimensional manifold with Euler characteristic 1 is the Real Projective Plane.  (One may also imagine this model as a discrete version of the Roman Surface....)
What's in the box:
xyz Projective Plane
6.8 x 6.8 x 6.8 cm
Switch to inches
2.68 x 2.68 x 2.68 inches
Switch to cm
Success Rate:
First To try.
What's this?
Mature audiences only.
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.