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ttokoro
21-Topaz I
ttokoro21-Topaz I
21-Topaz I
March 21, 2020
Solved

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

  • March 21, 2020
  • 2 replies
  • 3358 views

image.png

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

Best answer by ttokoro

Resistance of one resistor branch by Mathcad.

image.pngimage.png

2 replies

Derbigdog
Derbigdog15-Moonstone
15-Moonstone
March 21, 2020

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

ttokoro
21-Topaz I
ttokoro21-Topaz IAuthor
21-Topaz I
March 22, 2020

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. 

t.t.
-
-MFra-21-Topaz II
21-Topaz II
March 22, 2020

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.)

ttokoro
21-Topaz I
ttokoro21-Topaz IAuthor
21-Topaz I
March 22, 2020

 

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

t.t.
ttokoro
21-Topaz I
ttokoro21-Topaz IAuthorAnswer
21-Topaz I
March 24, 2020

Resistance of one resistor branch by Mathcad.

image.pngimage.png

t.t.
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