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

[ttokoro]

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

[Derbigdog]

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

[ttokoro]

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. 

[-MFra-]

Hi,

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

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.)

[ttokoro]

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 ValeryOchkov posted.

But, Solve diagonal resistance of resistor mesh

and this puzzle require the help of Mathcad to solve.

[ttokoro · Accepted solution]

Resistance of one resistor branch by Mathcad.

[ttokoro]