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Euler Characteristic of a Convex Polyhedron Calculator — result sheet
Check Euler’s V − E + F relation for a convex polyhedron from its vertices, edges, and faces.
Inputs used
Results
Visual chart
Breakdown
Calculation steps
Returned data table
Formula and methodology
Formula: Euler characteristic χ=V−E+F; a convex polyhedron has χ=2 and residual=χ−2.
Euler’s polyhedron relation gives a topology check for a closed, connected, convex polyhedral surface. The residual shows how far the entered counts are from the expected value of two.
This result follows the calculator's declared inputs, precision, validation boundaries, and model limits.
Input contract
- Vertices V — minimum 4; maximum 1000000000
- Edges E — minimum 4; maximum 1000000000
- Faces F — minimum 4; maximum 1000000000
Worked example
| Input | Value |
|---|---|
| Vertices V | 8 |
| Edges E | 12 |
| Faces F | 6 |
Euler characteristic =2; residual =0.
Assumptions and limits
- The counts describe one closed, connected convex polyhedron.
- Vertices, edges, and faces are whole-number counts.
- The tool checks the relation only; it does not reconstruct the solid or validate every face adjacency.
Calculator note
Source and methodology
Use the official WorldCalculate methodology policy for the source, formula, precision, and boundary standards behind this calculator.
Planning estimate, not financial, medical, legal, or professional advice. © WorldCalculate — reuse with attribution. Built and curated by Hassan ALRowaie.
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