Question:
What equations are used to create the TPMS types used in nTopology?
Answer:
Below is the table of standard TPMS available as Unit Cells with their corresponding equations. To build your own TPMS from an equation, go here.
Image 
Type 
Equation 

Gyroid  sin(x) cos(y) + sin(y) cos(z) + sin(z) cos(x)  
Schwarz  cos(x)+cos(y)+cos(z)  
Diamond  sin(x)*sin(y)*sin(z)+sin(x)*cos(y)*cos(z)+cos(x)*sin(y)*cos(z)+cos(x)*cos(y)*sin(z)  
Lidinoid  sin(2*x) * cos(y) * sin(z) + sin(2*y) * cos(z) * sin(x) + sin(2*z) * cos(x) * sin(y)  cos(2*x) * cos(2*y)  cos(2*y) * cos(2*z)  cos(2*z) * cos(2*x) + .3  
Split P  1.1*(sin(2*x)*sin(z)*cos(y)+sin(2*y)*sin(x)*cos(z)+sin(2*z)*sin(y)*cos(x))0.2*(cos(2*x)*cos(2*y)+cos(2*y)*cos(2*z)+cos(2*z)*cos(2*x))0.4*(cos(2*x) + cos(2*y) +cos(2*z))  
Neovius  3*(cos(x)+cos(y)+cos(z))+4*cos(x)*cos(y)*cos(z) 
Comments
Is there a way to create new tpms structures by inputting equations such as the ones above?
Yes, you can. Read more about it here: https://support.ntopology.com/hc/enus/articles/4403371438611
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