Homology Editor
Click edges and triangles to add or remove them from a simplicial complex. Watch β₀ (connected components) and β₁ (independent loops) update in real time. Three presets explore the triangle, the torus skeleton, and the Möbius strip.
Edge (active — click to remove)
Edge (inactive — click to add)
Triangle (active — click to remove)
Triangle (inactive — click to add)
Three vertices forming a loop. β₁=1 (one independent cycle). Fill the triangle to collapse the loop: β₁=0.
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Preset: Triangle. Active edges: 3 of 3. Active triangles: 0 of 1. β₀ = 1 (connected components), β₁ = 1 (independent loops). Three vertices forming a loop. β₁=1 (one independent cycle). Fill the triangle to collapse the loop: β₁=0.