When I get the following line "Top level object is a 3D object (manifold):" Beneath it is a field "Genus:" along with fields for "Vertices:" and "Facets:". Most of my models generate a Genus: of a small positive integer but some are zero and I just noticed one is -4 which makes me wonder what it could be.

I don't know from OpenSCAD, but Wikipedia says: https://en.wikipedia.org/wiki/Genus_(mathematics) > In mathematics > <https://en.wikipedia.org/wiki/Mathematics>, *genus* (pl.: *genera*) > has a few different, but closely related, meanings. Intuitively, the > genus is the number of "holes" of a surface > <https://en.wikipedia.org/wiki/Surface_(topology)>.^[1] > <https://en.wikipedia.org/wiki/Genus_(mathematics)#cite_note-FOOTNOTEPopescu-Pampu2016xiiiIntroduction-1> >  A sphere <https://en.wikipedia.org/wiki/Sphere> has genus 0, while > a torus <https://en.wikipedia.org/wiki/Torus> has genus 1. Some simple experiments yield results consistent with this definition. It does not mention the possibility of a negative number.  A Google search hints at a negative genus reflecting disconnected surfaces, and experiments are consistent with that, with three disconnected objects yielding a genus of -2.  (Though when I follow up on those Google hits, that's not what they say.  Still, the experiment is consistent with that interpretation.) And they appear to be added together, which doesn't make any intuitive sense to me.  One sphere plus two donuts equals zero. Manifold documentation says: https://manifoldcad.org/docs/html/classmanifold_1_1_manifold.html#a4b1e9ca27fc618965d0bbbc9d29fb5c1 > The genus is a topological property of the manifold, representing the > number of "handles". A sphere is 0, torus 1, etc. It is only > meaningful for a single mesh, so it is best to call Decompose() first. Decompose is: https://manifoldcad.org/docs/html/classmanifold_1_1_manifold.html#a7f20b130779680156ce0d28d91e5d106 > This operation returns a vector of Manifolds that are topologically > disconnected. If everything is connected, the vector is length one, > containing a copy of the original. It is the inverse operation of > Compose().

> And they appear to be added together, which doesn't make any intuitive sense to me. One sphere plus two donuts equals zero. Thanks! Your genus formula of adding holes and subtracting additional topologically disconnected manifolds works for my models. I probably could have come up with that through repeated tests but I'm glad I did not try too hard as it was making my brain hurt enough that I feared I would need a visit with doctor Gumby. On Fri, Mar 28, 2025 at 11:00 PM Jordan Brown <openscad@jordan.maileater.net> wrote: > I don't know from OpenSCAD, but Wikipedia says: > > https://en.wikipedia.org/wiki/Genus_(mathematics) > > In mathematics <https://en.wikipedia.org/wiki/Mathematics>, *genus* (pl.: > *genera*) has a few different, but closely related, meanings. > Intuitively, the genus is the number of "holes" of a surface > <https://en.wikipedia.org/wiki/Surface_(topology)>.[1] > <https://en.wikipedia.org/wiki/Genus_(mathematics)#cite_note-FOOTNOTEPopescu-Pampu2016xiiiIntroduction-1> > A sphere <https://en.wikipedia.org/wiki/Sphere> has genus 0, while a > torus <https://en.wikipedia.org/wiki/Torus> has genus 1. > > > Some simple experiments yield results consistent with this definition. > > It does not mention the possibility of a negative number. A Google search > hints at a negative genus reflecting disconnected surfaces, and experiments > are consistent with that, with three disconnected objects yielding a genus > of -2. (Though when I follow up on those Google hits, that's not what they > say. Still, the experiment is consistent with that interpretation.) > > And they appear to be added together, which doesn't make any intuitive > sense to me. One sphere plus two donuts equals zero. > > Manifold documentation says: > > https://manifoldcad.org/docs/html/classmanifold_1_1_manifold.html#a4b1e9ca27fc618965d0bbbc9d29fb5c1 > > The genus is a topological property of the manifold, representing the > number of "handles". A sphere is 0, torus 1, etc. It is only meaningful for > a single mesh, so it is best to call Decompose() first. > > > Decompose is: > > https://manifoldcad.org/docs/html/classmanifold_1_1_manifold.html#a7f20b130779680156ce0d28d91e5d106 > > This operation returns a vector of Manifolds that are topologically > disconnected. If everything is connected, the vector is length one, > containing a copy of the original. It is the inverse operation of Compose(). > > > > >