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

SOLVED
ttokoro
17-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)?

1 ACCEPTED SOLUTION

Accepted Solutions

Resistance of one resistor branch by Mathcad.

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View solution in original post

6 REPLIES 6

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

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. 

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.)

 

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

Resistance of one resistor branch by Mathcad.

image.pngimage.png

View solution in original post

image.png

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