Here's something I'm having trouble understanding, if someone can help
me understand I'd be very appreciative.

Here's a nifty way of drawing a cube with cut off corners.
But, it fails on the mirror of the corner at [1,1,1].

module corner(wid) {
corner_points = [[0,0,0],[1,0,0],[0,1,0],[0,0,1]];
corner_faces =  [[0,3,1],[0,2,3],[0,1,2],[1,3,2]];
polyhedron(wid*corner_points, corner_faces);
}

module cornercube(wid, cornerwid) {
cube_vertices = [[0,0,0],[0,0,1],[0,1,0],[0,1,1],
[1,0,0],[1,0,1],[1,1,0],[1,1,1]];
difference() {
cube(wid);
for (v = cube_vertices) {
#translate(wid*v) mirror(v) corner(cornerwid);
}
}
}
cornercube(20,5);

This code fixes things by handling that corner as a special case.
Can someone explain to me what's different about the one corner?
And is there some transformation that will work on all eight corners?

module cornercube2(wid,cornerwid) {
cube_vertices7 = [[0,0,0],[0,0,1],[0,1,0],[0,1,1],
[1,0,0],[1,0,1],[1,1,0]];
cube_vertices1 = [[1,1,1]];
difference() {
cube(wid);
for (v = cube_vertices7) {
translate(widv) mirror(v) corner(cornerwid);
}
for (v = cube_vertices1) {
#translate(widv) rotate([180,90,0]) corner(cornerwid);
}
}
}
cornercube2(20,5);

I don't have how to test this now. Have you tried to visualize just the
mirrored awkward corner? Something like:

translate(10*[1,1,1]) mirror ( [1,1,1]) corner(3);
% cube(10);

It's indeed a special case. If you transfer the original corner (red color)
DIRECTLY to its position  (i.e., w/o mirror()), and compare its relationship
with the one that is mirrored (teal color), you can see from the graph how
it is a special case :
http://forum.openscad.org/file/t602/180804_4_corner_mirroring_1.png

Instead of mirroring 7 times to all corners, mirroring application like this
can be better achieved by mirroring the original one (C0) to [x,0,0] corner
--- make it C1. Then, mirror BOTH C0-C1 to [0,y,0], generating 4 corners,
than again onto [0,0,z] to generate 8 corners:

module corners(wid=20, cornerwid=5)
{
module mirror_dir(d)
{
mps = [[1,0,0],[0,1,0],[0,0,1]];
children();                                  //<==== original copy
translate( wid*mps[d]) mirror( mps[d] ) children();  //<==== mirrored
copy
}

mirror_dir(2)
mirror_dir(1)
mirror_dir(0)
corner(cornerwid);
}
http://forum.openscad.org/file/t602/180804_4_corner_mirroring_2.png

This would be a very good general mirroring module for future 8-corner
mirroring.

$  Runsun Pan, PhD $ libs: scadx , doctest , faces ( git ), offline doc ( git ), runscad.py ( 2 , git ), editor of choice: CudaText  ( OpenSCAD lexer ); $ Tips ; $ Snippets

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Yeah Carsten,

a more convenient way to code this would be:

cornercube(20,5);
module octahedron(d = 10)
scale(dsqrt(3))
{
cylinder(r1=1, r2=0, h=sqrt(3).5, $fn=4);
scale([1,1,-1])cylinder(r1=1, r2=0, h=sqrt(3)*.5, $fn=4);
}

module cornercube(d=20, d1=5)
intersection()
{
cube(d, true);
octahedron(d-d1);
}

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Sorry, I miscalculated the height of the octahedron. It is as easy as this:

module octahedron(d = 10)
{
scale(d*sqrt(3))
{
cylinder(r1=1, r2=0, h=1, $fn=4);
scale([1,1,-1])cylinder(r1=1, r2=0, h=1, $fn=4);
}
}

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I don't think that using language primitives is "cheating", but I understand
what you mean. The main problem with the code given by the threadstarter is
that the cube is not centered. With a centered cube everything is clear and
easy.

Btw, there was another calculation error in my octahedron. I hope this the
final version:

module octahedron(d = 10)
{
x = d * 2 *sqrt(5)/3;
scale(x)
{
cylinder(r1=1, r2=0, h=1, $fn=4);
scale([1,1,-1])cylinder(r1=1, r2=0, h=1, $fn=4);
}
}

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