MANTRA 3-Manifolds | AHORN - Aachen Higher-Order Repository of Networks

The original MANTRA dataset includes both 2-manifolds and 3-manifolds. AHORN lists them as two separate datasets, with this page focusing on the 3-manifolds. You can find the 2-manifolds dataset here.

The MANTRA collection provides simplicial complexes built from triangulations of closed 2- and 3-manifolds. Each manifold is represented by its vertex set and list of simplices (triangles or tetrahedra), enabling topological and combinatorial experiments across two dimensions.

This dataset is derived from version 0.0.16 of MANTRA.

Dataset Statistics

Manifolds: 255,307
Simplices (all): 8,062,251

Size Distribution

Vertices per manifold

Min5

Q110

Median10

Q310

Max120

Simplices per manifold

Min5

Q129

Median31

Q332

Max600

Average Degree

Average Node Degree

Min4

Q111.6

Median12.4

Q312.8

Max24