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Solve diagonal resistance of resistor 3D mesh.

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Diagonal resistance of regular polyhedron. R(4)=1/2, R(6)=5/6. How about R(8), R(12) and R(20)?

ttokoroAnswer

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t.t.

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ValeryOchkov

24-Ruby IV

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-MFra-

21-Topaz II

Hi,

A simplification of the network topology allows you to easily apply Thevenin's theorem:

rete composta 2.jpg

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ttokoro

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ttokoro

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21-Topaz I

The diagonal resistance of resistor 3D mesh is 5/6 ohm.

How about 1*2 3D Mesh?

Each branch resister is 1 ohm.

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ttokoro

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ttokoro

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21-Topaz I

i=2: 1*1*1

i=3: 1*1*2

i=4: 1*1*3....

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ttokoro

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ttokoro

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ppal_255687

18-Opal

I don't know why every body went to town on this. You already gave the V and I so R = 5/6 ohms.

But as an academic exercise - as others have given but more colourful pictures are here:

https://www.rfcafe.com/miscellany/factoids/resistor-cube-equivalent-resistance-kirts-cogitations-256.htm

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ttokoro

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This is not solving 3D 1*1*1 grid resistor mesh only. Using Mathcad or other mathematical programs we can calculate more interesting resistor grid problems.

1/3+1/6+1/3 can not use if the grid is 1*1*2. I post many unique resistor grid problems here. This time 60 node soccer ball resistor grid result is shown. Please try to solve it because I can not find any answer in WWW sites. Without using Math software, we can not solve such as R1-2 of resistor ball.

1*1*2 1*1*1

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ppal_255687

18-Opal

https://inst.eecs.berkeley.edu/~ee100/fa04/lecture_notes/EE100supplementarynote_week04-3.pdf

good starting point

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-MFra-

21-Topaz II

What do you think of my solution? Maybe I took the wrong node as a reference point?

2RBridges 0.jpg 2RBridges 1.jpg 2RBridges 2.jpg 2RBridges 3.jpg 2RBridges 4.jpg 2RBridges 5.jpg 2RBridges 6.jpg 2RBridges 7.jpg 2RBridges 9.jpg 2RBridges 10.jpg

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ttokoro

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I will check your circuit. Please upload your Mathcad worksheet. I use Prime 9 to solve it.

I view your post and I understand this is 3D cube circuit with 12 one ohms to find the equivalent resistance of diagonal nodes. Node method is used to solve the circuit. I think this is the best method to solve the resistance.

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-MFra-

21-Topaz II

Hi,
Undoubtedly, I made some mistakes. As for the theory, I was inspired by some texts including: "Linesr and non linear circuits" by L. O. Chua, C. A. Desoer, E. S. Kuh, for the construction of the TABLEAU matrix. You can find my worksheet attached.
Greetings

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1_Rete-resistiva-3D.zip

ttokoro

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21-Topaz I

3.4.5 ohms cube.

1 ohm circuit by 1 ohms. Each 1 ohm has different current when apply 1A for 1 and 13 nodes.

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ttokoro

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Diagonal resistances of n-D cubes. AI only knows 3D and 4D ones.

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ttokoro

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Source and Image Credits: Ellenberg, J., Libedinsky, N., Plaza, D., Simental, J., & Williamson, G. (2026). Bruhat intervals that are large hypercubes.

New hyper cube circuit 2026.