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nHOLED TORUS
The notion of nholed torus, or ntorus, or nuple torus, or sphere with n handles, refers to any topological space homeomorphic to the connected sum of the simple torus n times with itself: ; by convention, we set .
Any orientable connected compact surface without boundary is homeomorphic to an ntorus.
The Euler characteristic of the ntorus is equal to 2–2n.
The double torus is informally called "pretzel". On the right, a mathematical pretzel composed of two loops that are Viviani curves and an arc of a circle. 
An algebraic pretzel of degree 4, with 2 planes of symmetry, and equation ; this equation was knocked up from that of the figureeight: , in order to thicken it.  
Starting from the lemniscate of Bernoulli, we get the figure below, with equation:
. 

A triple algebraic torus, based on the regular trifolium, with equation: .  
A quadruple algebraic torus, with equation: . 
The nholed torus is also informally called "fougasse": opposite, a fougasse with 6 holes. 

Do not mistake the ntorus with the ndimensional torus,; in particular, .
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© Robert FERRÉOL 2017