Fig. 1 | Scientific Reports

Fig. 1

From: Computing Euler characteristic of \({N}\)-dimensional objects via a Skyrmion-inspired overlaying (\({N}\)+1)-dimensional chiral field

Fig. 1

Generating a chiral vector field from an object and computing its Euler characteristic. (a–c) Illustrations of (a) a given example object, (b) an initial \(\:\tilde S\) configuration, and (c) a generated chiral \(\:\tilde S\) configuration. (d) A chiral vector mapped onto a shared origin. The vertices of cones in (b-d) indicate the direction of vectors. (e,f) Schematic representations of the partitioning simplexes from (e) a square in two-dimensional space and (f) a cube in three-dimensional space. (g) A hypercube in four dimensions. The \(\:{\tilde S}_{i}s\) shown in (e,f) denote the \(\:\tilde S\)s located at the vertices of a single simplex for each dimensional case, where the \(\:i\) denote the sequence of vertices connected to form a simplex. Blender version 3.6 was used to generate the 3D representations in (b–d).

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