# General Formula Resistors Polyhedron

• luiseduardo
In summary, there is a method for finding the equivalent resistance between two opposite points of a regular polyhedron with all resistors equal to R. By drawing a graph of the polyhedron and marking points at different distances from an arbitrary terminal, it is possible to determine the total resistance. However, this method does not work for a tetrahedron. For a dodecahedron, the total resistance can be calculated using a specific formula. Care must be taken when sharing this information, as it may be seen as helping with homework.

#### luiseduardo

Hello all,

Does anyone know of any general formula for the equivalent resistance between two opposite points of a regular polyhedron (cube, dodecahedron ..) with all the resistors equal to R?

draw a graph of the polyhedron. choose an arbitrary point as one of the terminals. Now mark all points that are 1 resistance away from this, then all points that are at distance 2, etc.
you should get 1 point at maximum distance, which is the other terminal.
(this won't work for a tetrahedron, because there is no opposite point)

All points at the same distance, will have the same voltage, because of symmetry, so you can connect them with wires. The resulting network can easily be solved by replacing series and paralles resistances, because all resistances from an n to an n+1 distance point will now be parallel

for a dodecaedron, I get

3 points at distance 1
6 points at distance 2
6 points at distance 3
3 ponts at distance 4
1 point at distance 5

3 resistances between distance 0 and distance 1 points
6 resistances between distance 1 and distance 2 points
6 resistances between distance 2 and distance 3 points
6 resistances between distance 3 and distance 4 points
3 resistances between distance 4 and distance 5 points

6 resistances between points of equal distance, which will carry no current

so the total resistance is (1/3+1/6+1/6+1/6+1/3)R = (7/6)R

Careful, I once drew an infraction for answering the cube problem, on the grounds it was "homework"! :rofl:

Thanks, but do you know a general formula ?

## 1. What is a General Formula Resistors Polyhedron?

A General Formula Resistors Polyhedron is a mathematical model used in electrical engineering to represent the behavior of resistors in a circuit. It takes into account the resistance, voltage, and current of the resistor to determine its overall behavior.

## 2. How is a General Formula Resistors Polyhedron different from a regular resistor?

A regular resistor is a physical component that has a specific resistance value. A General Formula Resistors Polyhedron, on the other hand, is a mathematical model that can represent the behavior of various resistors with different values in a circuit.

## 3. How is a General Formula Resistors Polyhedron used in circuit analysis?

A General Formula Resistors Polyhedron is used to calculate the voltage, current, and resistance of a resistor in a circuit. It can also be used to determine the power dissipation and heat generation of a resistor.

## 4. Are General Formula Resistors Polyhedrons accurate?

Yes, General Formula Resistors Polyhedrons are accurate as they are based on mathematical equations and take into account all the relevant variables of a resistor in a circuit.

## 5. Can General Formula Resistors Polyhedrons be used for all types of resistors?

Yes, General Formula Resistors Polyhedrons can be used for all types of resistors, including fixed resistors, variable resistors, and even non-linear resistors. However, the accuracy may vary depending on the complexity of the resistor's behavior.