Midsphere Radius of Hexakis Octahedron Calculator

✖Long Edge of Hexakis Octahedron is the length of the long edge of any of the congruent triangular faces of the Hexakis Octahedron.ⓘ Long Edge of Hexakis Octahedron [l_e(Long)]

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✖Midsphere Radius of Hexakis Octahedron is defined as the radius of the sphere for which all the edges of the Hexakis Octahedron become a tangent line on that sphere.ⓘ Midsphere Radius of Hexakis Octahedron [r_m]

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Formula

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Midsphere Radius of Hexakis Octahedron

Formula

`"r"_{"m"} = ("l"_{"e(Long)"}/4)*(1+(2*sqrt(2)))`

Example

`"19.14214m"=("20m"/4)*(1+(2*sqrt(2)))`

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Midsphere Radius of Hexakis Octahedron Solution

STEP 0: Pre-Calculation Summary

Formula Used

Midsphere Radius of Hexakis Octahedron = (Long Edge of Hexakis Octahedron/4)*(1+(2*sqrt(2)))
r_m = (l_e(Long)/4)*(1+(2*sqrt(2)))
This formula uses 1 Functions, 2 Variables

Functions Used

sqrt - A square root function is a function that takes a non-negative number as an input and returns the square root of the given input number., sqrt(Number)

Variables Used

Midsphere Radius of Hexakis Octahedron - (Measured in Meter) - Midsphere Radius of Hexakis Octahedron is defined as the radius of the sphere for which all the edges of the Hexakis Octahedron become a tangent line on that sphere.
Long Edge of Hexakis Octahedron - (Measured in Meter) - Long Edge of Hexakis Octahedron is the length of the long edge of any of the congruent triangular faces of the Hexakis Octahedron.

STEP 1: Convert Input(s) to Base Unit

Long Edge of Hexakis Octahedron: 20 Meter --> 20 Meter No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

r_m = (l_e(Long)/4)*(1+(2*sqrt(2))) --> (20/4)*(1+(2*sqrt(2)))

Evaluating ... ...

r_m = 19.142135623731

STEP 3: Convert Result to Output's Unit

19.142135623731 Meter --> No Conversion Required

FINAL ANSWER

19.142135623731 ≈ 19.14214 Meter <-- Midsphere Radius of Hexakis Octahedron

(Calculation completed in 00.020 seconds)

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< 8 Midsphere Radius of Hexakis Octahedron Calculators

Midsphere Radius of Hexakis Octahedron given Surface to Volume Ratio

Go Midsphere Radius of Hexakis Octahedron = ((1+(2*sqrt(2)))/4)*((12*sqrt(543+(176*sqrt(2))))/(Surface to Volume Ratio of Hexakis Octahedron*(sqrt(6*(986+(607*sqrt(2)))))))

Midsphere Radius of Hexakis Octahedron given Total Surface Area

Go Midsphere Radius of Hexakis Octahedron = ((1+(2*sqrt(2)))/4)*(sqrt((7*Total Surface Area of Hexakis Octahedron)/(3*sqrt(543+(176*sqrt(2))))))

Midsphere Radius of Hexakis Octahedron given Truncated Cuboctahedron Edge

Go Midsphere Radius of Hexakis Octahedron = ((1+(2*sqrt(2)))/4)*(2/7)*(sqrt(60+(6*sqrt(2))))*(Truncated Cuboctahedron Edge of Hexakis Octahedron)

Midsphere Radius of Hexakis Octahedron given Insphere Radius

Go Midsphere Radius of Hexakis Octahedron = ((1+(2*sqrt(2)))/4)*((2*Insphere Radius of Hexakis Octahedron)/(sqrt((402+(195*sqrt(2)))/194)))

Midsphere Radius of Hexakis Octahedron given Volume

Go Midsphere Radius of Hexakis Octahedron = ((1+(2*sqrt(2)))/4)*(((28*Volume of Hexakis Octahedron)/(sqrt(6*(986+(607*sqrt(2))))))^(1/3))

Midsphere Radius of Hexakis Octahedron given Short Edge

Go Midsphere Radius of Hexakis Octahedron = ((1+(2*sqrt(2)))/4)*((14*Short Edge of Hexakis Octahedron)/(10-sqrt(2)))

Midsphere Radius of Hexakis Octahedron

Go Midsphere Radius of Hexakis Octahedron = (Long Edge of Hexakis Octahedron/4)*(1+(2*sqrt(2)))

Midsphere Radius of Hexakis Octahedron given Medium Edge

Go Midsphere Radius of Hexakis Octahedron = (7*Medium Edge of Hexakis Octahedron)/6

Midsphere Radius of Hexakis Octahedron Formula

Midsphere Radius of Hexakis Octahedron = (Long Edge of Hexakis Octahedron/4)*(1+(2*sqrt(2)))
r_m = (l_e(Long)/4)*(1+(2*sqrt(2)))

What is Hexakis Octahedron?

In geometry, a Hexakis Octahedron (also called hexoctahedron, disdyakis dodecahedron, octakis cube, octakis hexahedron, kisrhombic dodecahedron), is a Catalan solid with 48 congruent triangular faces, 72 edges and 26 vertices. It is the dual of the Archimedean solid ‘truncated cuboctahedron’. As such it is face-transitive but with irregular face polygons.

How to Calculate Midsphere Radius of Hexakis Octahedron?

Midsphere Radius of Hexakis Octahedron calculator uses Midsphere Radius of Hexakis Octahedron = (Long Edge of Hexakis Octahedron/4)*(1+(2*sqrt(2))) to calculate the Midsphere Radius of Hexakis Octahedron, The Midsphere Radius of Hexakis Octahedron formula is defined as the radius of the sphere for which all the edges of the Hexakis Octahedron become a tangent line on that sphere. Midsphere Radius of Hexakis Octahedron is denoted by r_m symbol.

How to calculate Midsphere Radius of Hexakis Octahedron using this online calculator? To use this online calculator for Midsphere Radius of Hexakis Octahedron, enter Long Edge of Hexakis Octahedron (l_e(Long)) and hit the calculate button. Here is how the Midsphere Radius of Hexakis Octahedron calculation can be explained with given input values -> 19.14214 = (20/4)*(1+(2*sqrt(2))).

FAQ

What is Midsphere Radius of Hexakis Octahedron?

The Midsphere Radius of Hexakis Octahedron formula is defined as the radius of the sphere for which all the edges of the Hexakis Octahedron become a tangent line on that sphere and is represented as r_m = (l_e(Long)/4)*(1+(2*sqrt(2))) or Midsphere Radius of Hexakis Octahedron = (Long Edge of Hexakis Octahedron/4)*(1+(2*sqrt(2))). Long Edge of Hexakis Octahedron is the length of the long edge of any of the congruent triangular faces of the Hexakis Octahedron.

How to calculate Midsphere Radius of Hexakis Octahedron?

The Midsphere Radius of Hexakis Octahedron formula is defined as the radius of the sphere for which all the edges of the Hexakis Octahedron become a tangent line on that sphere is calculated using Midsphere Radius of Hexakis Octahedron = (Long Edge of Hexakis Octahedron/4)*(1+(2*sqrt(2))). To calculate Midsphere Radius of Hexakis Octahedron, you need Long Edge of Hexakis Octahedron (l_e(Long)). With our tool, you need to enter the respective value for Long Edge of Hexakis Octahedron and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well.

How many ways are there to calculate Midsphere Radius of Hexakis Octahedron?

In this formula, Midsphere Radius of Hexakis Octahedron uses Long Edge of Hexakis Octahedron. We can use 7 other way(s) to calculate the same, which is/are as follows -

Midsphere Radius of Hexakis Octahedron = (7*Medium Edge of Hexakis Octahedron)/6
Midsphere Radius of Hexakis Octahedron = ((1+(2*sqrt(2)))/4)*((14*Short Edge of Hexakis Octahedron)/(10-sqrt(2)))
Midsphere Radius of Hexakis Octahedron = ((1+(2*sqrt(2)))/4)*(sqrt((7*Total Surface Area of Hexakis Octahedron)/(3*sqrt(543+(176*sqrt(2))))))
Midsphere Radius of Hexakis Octahedron = ((1+(2*sqrt(2)))/4)*(((28*Volume of Hexakis Octahedron)/(sqrt(6*(986+(607*sqrt(2))))))^(1/3))
Midsphere Radius of Hexakis Octahedron = ((1+(2*sqrt(2)))/4)*((2*Insphere Radius of Hexakis Octahedron)/(sqrt((402+(195*sqrt(2)))/194)))
Midsphere Radius of Hexakis Octahedron = ((1+(2*sqrt(2)))/4)*((12*sqrt(543+(176*sqrt(2))))/(Surface to Volume Ratio of Hexakis Octahedron*(sqrt(6*(986+(607*sqrt(2)))))))
Midsphere Radius of Hexakis Octahedron = ((1+(2*sqrt(2)))/4)*(2/7)*(sqrt(60+(6*sqrt(2))))*(Truncated Cuboctahedron Edge of Hexakis Octahedron)

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