Archive · 30 Sep 2026
Mathematician Describes Eight-Faced Genus-3 Polyhedron With Three Holes
A mathematician named Ruslan Mizhaev has described a very unusual 3D shape.
It has eight flat faces, 26 edges, and 24 corners.
The shape also has three holes passing through it.
Every pair of faces touches along at least one edge.
Some pairs share one edge, while others share two.
Exactly three faces meet at each corner.
Mathematicians call this kind of object a genus-3 polyhedron.
The study helps explore connections between geometry, graph theory, and topology, but it has not yet been checked by scientific reviewers.
Ruslan Mizhaev has described a genus-3 polyhedron with eight faces and three holes.
The shape has 26 edges and 24 vertices, or corners.
Every pair of faces shares at least one edge.
Twenty face pairs share one edge, while eight pairs share two edges.
The work is currently a preprint and has not been peer-reviewed or published in a scientific journal.
- Who
- Mathematician Ruslan Mizhaev.
- What
- A description of a genus-3 polyhedron with eight faces, 26 edges, 24 vertices, and three holes.
- When
- The article does not specify a date for the work.
- Where
- The geometry is described in a preprint study covered by New Scientist.
- Why
- The study examines relationships among combinatorial topology, graph theory, and three-dimensional geometry.
- Faces
- 8
- Edges
- 26
- Vertices
- 24
- Holes
- 3
- Face-pair connections
- 20 pairs share one edge; 8 pairs share two edges
- Faces at each vertex
- Exactly 3
- Publication status
- Preprint; not yet peer-reviewed or published in a scientific journal