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Euler Characteristic

The Euler characteristic is a topological invariant, a number that describes a topological space's shape or structure regardless of the way it is bent.

The Euler characteristic equals the number of vertices plus the number of faces divided by the number of edges.

Formula

QuantityVariable["χ", "Unitless"] == -QuantityVariable["D", "Unitless"] + QuantityVariable["F", "Unitless"] + QuantityVariable["V", "Unitless"]

symbol description physical quantity
χ Euler characteristic "Unitless"
D edges "Unitless"
F faces "Unitless"
V vertices "Unitless"

Forms

Examples

Get the resource:

In[1]:=
ResourceObject["Euler Characteristic"]
Out[1]=

Get the formula:

In[2]:=
FormulaData[ResourceObject["Euler Characteristic"]]
Out[2]=

Use some values:

In[3]:=
FormulaData[ ResourceObject[ "Euler Characteristic"], {QuantityVariable["F","Unitless"] -> 6, QuantityVariable["V","Unitless"] -> 8, QuantityVariable["\[Chi]","Unitless"] -> 2}]
Out[3]=

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