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Clebsch Diagonal Cubic With 2 Planes

by MO-Labs

Clebsch Diagonal Cubic With 2 Planes 3d printed
Clebsch Diagonal Cubic With 2 Planes 3d printed
Clebsch Diagonal Cubic With 2 Planes 3d printed

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Sandstone

Full Color Sandstone
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  • 3D printed just for you.
  • Full Color Sandstone: Fully colored material with a coarse finish and a delicate feel.
$219.90
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About this Product

One of the most classical models in mathematics is the Clebsch Diagonal Surface. As any smooth cubic surface, it contains 27 lines, but for this special surface, all 27 lines are real, and very symmetric. In addition, the object shows two planes which cut the surface in one line and three lines, respectively. Some mathematics details: The model illustrates part of the proof of the fact that any cubic surface contains 27 lines: Let us assume that we know that any such surface contains at least one line. One may consider all planes through this line. Any such plane cuts the given cubic surface in a cubic plane curve which factors into a line and a conic. It turns out that it happens exactly 5 times that the conic is not smooth, but factors itself into 2 lines. With some other arguments, this can be used to prove that there are exactly 27 lines.
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Clebsch Diagonal Cubic With 2 Planes in Full Color Sandstone
Width Height Depth
11.136 cm 17.542 cm 11.134 cm
This model is 3D Printed in Full Color Sandstone: Fully colored material with a coarse finish and a delicate feel.
Model version 1 | Last updated on 02/26/2015

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Choose a Material

Sandstone

Full Color Sandstone
OVERVIEW
  • 3D printed just for you.
  • Full Color Sandstone: Fully colored material with a coarse finish and a delicate feel.
$219.90
Secure Checkout
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