MANTRA 3-Manifolds
Network Type
Overview
Note
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.
Network Metadata
Each network includes the following metadata:
betti_numbers, e.g.,[1, 0, 0, 1]torsion_coefficients, e.g.,["", "", "Z_2", ""]namegenusorientablevertex_transitive
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