MANTRA 2-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 2-manifolds. You can find the 3-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, 1]torsion_coefficients, e.g.,["", "Z_2", ""]namegenusorientablevertex_transitive
Statistics
Manifolds
43,214
Simplices (all)
992,948
Size Distribution
Vertices per manifold
Min4
Q110
Median10
Q310
Max15
Simplices per manifold
Min4
Q122
Median24
Q324
Max60
Average Degree
Average Node Degree
Min3
Q16.6
Median7.2
Q37.2
Max12