Meissner polyhedra are solids of constant width that generalize the Meissner tetrahedra. They are three-dimensional analogs of Reuleaux polygons (Bogosel 2023). Their boundaries consist of pieces of spheres and spindle tori (Hynd 2023). Bogosel (2023) constructed Meissner polyhedra up to 14 vertices.

# Meissner Polyhedron

## See also

Meissner Tetrahedra## Explore with Wolfram|Alpha

## References

Bogosel, B. "Volume Computation for Meissner Polyhedra and Applications." 25 Oct 2023. https://arxiv.org/abs/2310.17672.Hynd, R. "The Density of Meissner Polyhedra."*Geom. Dedicata*2018:89, 1-50, 2024.

## Cite this as:

Weisstein, Eric W. "Meissner Polyhedron."
From *MathWorld*--A Wolfram Web Resource. https://mathworld.wolfram.com/MeissnerPolyhedron.html