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ttokoro
21-Topaz I
ttokoro21-Topaz I
21-Topaz I
March 20, 2020
Solved

Solve diagonal resistance of resistor 3D mesh.

  • March 20, 2020
  • 10 replies
  • 22248 views

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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)?

    Best answer by ttokoro

    image.pngimage.png

    10 replies

    V
    24-Ruby IV
    ValeryOchkov24-Ruby IV
    24-Ruby IV
    March 20, 2020

    Cube.png

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

    Hi,

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

    rete composta 2.jpg

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

    image.pngimage.png

    t.t.
    ttokoro
    21-Topaz I
    ttokoro21-Topaz IAuthor
    21-Topaz I
    September 2, 2020

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

    How about 1*2 3D Mesh?

    image.png

    Each branch resister is 1 ohm. 

    t.t.
    ttokoro
    21-Topaz I
    ttokoro21-Topaz IAuthor
    21-Topaz I
    September 8, 2020

    image.png

    image.png

    t.t.
    ttokoro
    21-Topaz I
    ttokoro21-Topaz IAuthor
    21-Topaz I
    September 9, 2020

    image.pngimage.png

    i=2:    1*1*1

    i=3:    1*1*2

    i=4:    1*1*3....

    t.t.
    ttokoro
    21-Topaz I
    ttokoro21-Topaz IAuthor
    21-Topaz I
    July 10, 2021

    image.png

    t.t.
    ttokoro
    21-Topaz I
    ttokoro21-Topaz IAuthor
    21-Topaz I
    July 31, 2021

    image.pngimage.png

    t.t.
    P
    ppal_25568718-Opal
    18-Opal
    February 21, 2022

    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

     

    ttokoro
    21-Topaz I
    ttokoro21-Topaz IAuthor
    21-Topaz I
    February 21, 2022

    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. 

     

    image.pngimage.pngimage.png

    1*1*2                                                                                        1*1*1

    t.t.
    P
    ppal_25568718-Opal
    18-Opal
    February 21, 2022

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

    good starting point

    -
    -MFra-21-Topaz II
    21-Topaz II
    March 15, 2023

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

    2RBridges 0.jpg2RBridges 1.jpg2RBridges 2.jpg2RBridges 3.jpg2RBridges 4.jpg2RBridges 5.jpg2RBridges 6.jpg2RBridges 7.jpg2RBridges 5.jpg2RBridges 9.jpg2RBridges 10.jpg

    ttokoro
    21-Topaz I
    ttokoro21-Topaz IAuthor
    21-Topaz I
    March 15, 2023

    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.

    image.pngimage.pngimage.pngimage.png

    t.t.
    -
    -MFra-21-Topaz II
    21-Topaz II
    March 16, 2023

    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

    ttokoro
    21-Topaz I
    ttokoro21-Topaz IAuthor
    21-Topaz I
    April 19, 2025

    3.4.5 ohms cube.

    Pyta-345.jpeg

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

    1ohmby1ohms_3D.jpeg

    t.t.
    ttokoro
    21-Topaz I
    ttokoro21-Topaz IAuthor
    21-Topaz I
    December 20, 2025

    image.png

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

    t.t.
    ttokoro
    21-Topaz I
    ttokoro21-Topaz IAuthor
    21-Topaz I
    December 25, 2025

    image.pngimage.pngimage.png

    t.t.
    ttokoro
    21-Topaz I
    ttokoro21-Topaz IAuthor
    21-Topaz I
    January 24, 2026

    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.

    HyperCube20262.jpgHyperCube2026-2.jpg

    t.t.
    ttokoro
    21-Topaz I
    ttokoro21-Topaz IAuthor
    21-Topaz I
    January 28, 2026

    12-5x6.jpg

    ttokoro_0-1769594411535.png

     

    t.t.
    ttokoro
    21-Topaz I
    ttokoro21-Topaz IAuthor
    21-Topaz I
    February 21, 2026

    Diagonal resistance of Galileo's 12-20 cube cauldron at the Milan Olympics.

    image.pngimage.pngimage.png

    t.t.
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