Verify version as stl export works only if version ≥ 7.6.beta3
Definition of the polyhedron
Define t
as the name for the variable for polynomials of one variable and rational coefficients.
Define where
Compute the roots of in the set of -algebraic real numbers.
Define as the third root.
Define where
Compute the roots of in the set of -algebraic real numbers and define as the square root of the largest root of .
Define where $F_{z^2}(t) = − 881721 + 14088624t − 507815656t^2 + 22228266304t^3 − 345876361600t^4
2163078191936t^5 − 5229062814592t^6 + 2885777661952t^7 + 604100406528t^8 + 284044459008t^9 − 1111813844992t^{10} + 65086242816t^{11} + 157070950400t^{12}$
Compute the roots of in the set of -algebraic real numbers and define as the square root of the second largest root of .
Define the polyhedron as the convex hull of the following set of points:
Plot as SageMath's stl
export works only from graphics objects
Side note: polar dual
Search good position for the printing.
The 3d printer cannot print on air. That's why any polyhedron passed to the printer should be lying down on one of it's faces. Slicer software, which helps to convert stl
files to the gcode
needed by the printer can usually take care of this step. But as we had some troubles with our slicing step, we also tried to put the polyhedron in a correct position before slicing it.
Option 1 : Cut in two parts
A first try could be to try to cut by a horizontal plane. Then, the two parts are the same because of the symmetries of the polyhedron and the top half is lying flat.
Unfortunately this cut did not work out well in printing because the very top corner is too sharp. The 3d printer has usually some troubles with cusps pointing upwards.
Option 2 : Rotate the polygon to put it flat
Compute the normal vector of the face that will be put flat
Option 3 : Ask Slic3r to do the job.
Unfortunately, the graphical interface of the recent version of Slic3r do not work on (my) Linux Debian. Using it from the command line turned out to be not really evident. This is kind of sad because Slic3r's has a handy "Lay flat" button which works very well - at least for objects with low number of faces, as this one. This finally worked – on a borrowed Windows computer…
G
is a group of graphical objects. The last element in the group is an IndexFaceSet and can be saved to stl
file.