This new pip-installable package, https://pypi.org/project/passagemath-polymake/, is part of the set of Python packages of https://github.com/passagemath that together provide the full functionality of SageMath.

"pip install -v passagemath-polymake" installs Perl, Perl prerequisites of polymake ...

passagemath-polyhedra (https://pypi.org/project/passagemath-polyhedra/) is one of the pip-installable components of the modularized SageMath library, developed by the passagemath project. It supports CPython 3.9-3.13 on Linux and macOS and provides binary wheels for these platforms on PyPI ...

You are probably aware of this, and it is probably part of what you mean in the documentation with "limited support" for polyhedra over quadratic extensions, but I thought I should report it:
polytope > $p = new Polytope<QuadraticExtension>(EQUATIONS=>[[1,2,3]], INEQUALITIES=>[[1,0,0]]);

polytope ...

Thank you, this workaround works. Code is at: https://trac.sagemath.org/ticket/22723

Anyway, "just another special case". I'll work around it.

I think this is the wrong conclusion. The point is that your "AFFINE_HULL" does not fit the description of the empty polytope.

Please try the following:

> $p = new Polytope(EQUATIONS=>[[-1, 0, 0]], INEQUALITIES=>[]);
> $p->FACETS;
> $p ...

The attached polyhedron whose H-rep uses QuadraticExtension crashes polymake (segfault) when I try to compute the vertices.
This is with Polymake 3.1 on Mac OS X, compiled within Sage using the minimal tarball. Simpler calculations, including some with QuadraticExtension, seem to work fine with this ...

Anyway, "just another special case". I'll work around it.

Wait! The input data is not consistent. The polytope apparently is supposed to live in 2-space. If the affine hull of the polytope is given by just on linear equation it must be 1-dimensional. The corresponding rule, which is actually triggered, is correct.

Please use "input properties" instead ...

Welcome to polymake version 3.1
[...]
Application polytope currently uses following third-party software packages:
4ti2, bliss, cdd, latte, libnormaliz, lrs, permlib, ppl, singular, sketch, sympol, threejs, tikz, tosimplex
polytope > $p = new Polytope(VERTICES=>[], LINEALITY_SPACE=>[], AFFINE_HULL ...

So what's happening here is simply that GMP and other libraries are built for one architecture only, whereas "perl -MExtUtils::Embed -e ccflags" gives flags that build for two architectures at the time.
Just a quick follow-up. I have just found an easier workaround that does not require patching ...