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Solve the resistance of one resistor of regular polyhedron 3D mesh.

SOLVED
ttokoro
Peridot

Solve the resistance of one resistor of regular polyhedron 3D mesh.

image.png

R(4)=1/2, R(6)=7/12. How about R(8), R(12) and R(20)?

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Accepted Solutions

Re: Solve the resistance of one resistor of regular polyhedron 3D mesh.

Resistance of one resistor branch by Mathcad.

image.pngimage.png

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6 REPLIES 6

Re: Solve the resistance of one resistor of regular polyhedron 3D mesh.

This is a very old problem and I believe the answer is, the equivalent resistance is 1 Ohm.

Re: Solve the resistance of one resistor of regular polyhedron 3D mesh.

Yes, all resistances of each branch is 1 ohm as shown in my picture. The question is the eqivarent registane of one branch of the regular polyhedrons such as regular tetrahedron=1/2 as shown in my question. 

Re: Solve the resistance of one resistor of regular polyhedron 3D mesh.

Hi,

You could do the analysis, in the more general case considering the following equivalent network:

superbridge.jpg

to simplify, you could use the star-triangle transformation and see if it is possible to determine the equivalent impedance.

(Sorry, I'm referring to your previous 3D network question with the voltage generator.)

Re: Solve the resistance of one resistor of regular polyhedron 3D mesh.

 

Thanks. Your case is a diagonal resistance of regular polyhedron surface. 

Regular hexahedron shows 3/4 ohm. I am using current generator of 1 A.

So V=IR =R shows the resistance itself. 

My another puzzle Solve diagonal resistance of resistor 3D mesh

can solve by your answer and also  posted.

But, Solve diagonal resistance of resistor mesh

and this puzzle require the help of Mathcad to solve.

 

image.png

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Re: Solve the resistance of one resistor of regular polyhedron 3D mesh.

Resistance of one resistor branch by Mathcad.

image.pngimage.png

View solution in original post

Tags (1)

Re: Solve the resistance of one resistor of regular polyhedron 3D mesh.

image.png

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