Insphere 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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✖Insphere Radius of Hexakis Octahedron is defined as the radius of the sphere that is contained by the Hexakis Octahedron in such a way that all the faces just touching the sphere.ⓘ Insphere Radius of Hexakis Octahedron [r_i]

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Formula

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Insphere Radius of Hexakis Octahedron

Formula

`"r"_{"i"} = ("l"_{"e(Long)"}/2)*(sqrt((402+(195*sqrt(2)))/194))`

Example

`"18.69136m"=("20m"/2)*(sqrt((402+(195*sqrt(2)))/194))`

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Insphere Radius of Hexakis Octahedron Solution

STEP 0: Pre-Calculation Summary

Formula Used

Insphere Radius of Hexakis Octahedron = (Long Edge of Hexakis Octahedron/2)*(sqrt((402+(195*sqrt(2)))/194))
r_i = (l_e(Long)/2)*(sqrt((402+(195*sqrt(2)))/194))
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

Insphere Radius of Hexakis Octahedron - (Measured in Meter) - Insphere Radius of Hexakis Octahedron is defined as the radius of the sphere that is contained by the Hexakis Octahedron in such a way that all the faces just touching the 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_i = (l_e(Long)/2)*(sqrt((402+(195*sqrt(2)))/194)) --> (20/2)*(sqrt((402+(195*sqrt(2)))/194))

Evaluating ... ...

r_i = 18.6913570172352

STEP 3: Convert Result to Output's Unit

18.6913570172352 Meter --> No Conversion Required

FINAL ANSWER

18.6913570172352 ≈ 18.69136 Meter <-- Insphere Radius of Hexakis Octahedron

(Calculation completed in 00.004 seconds)

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< 8 Insphere Radius of Hexakis Octahedron Calculators

Insphere Radius of Hexakis Octahedron given Surface to Volume Ratio

Go Insphere Radius of Hexakis Octahedron = ((sqrt((402+(195*sqrt(2)))/194))/2)*((12*sqrt(543+(176*sqrt(2))))/(Surface to Volume Ratio of Hexakis Octahedron*(sqrt(6*(986+(607*sqrt(2)))))))

Insphere Radius of Hexakis Octahedron given Total Surface Area

Go Insphere Radius of Hexakis Octahedron = ((sqrt((402+(195*sqrt(2)))/194))/2)*(sqrt((7*Total Surface Area of Hexakis Octahedron)/(3*sqrt(543+(176*sqrt(2))))))

Insphere Radius of Hexakis Octahedron given Truncated Cuboctahedron Edge

Go Insphere Radius of Hexakis Octahedron = ((sqrt((402+(195*sqrt(2)))/194))/2)*(2/7)*(sqrt(60+(6*sqrt(2))))*(Truncated Cuboctahedron Edge of Hexakis Octahedron)

Insphere Radius of Hexakis Octahedron given Volume

Go Insphere Radius of Hexakis Octahedron = ((sqrt((402+(195*sqrt(2)))/194))/2)*(((28*Volume of Hexakis Octahedron)/(sqrt(6*(986+(607*sqrt(2))))))^(1/3))

Insphere Radius of Hexakis Octahedron given Midsphere Radius

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

Insphere Radius of Hexakis Octahedron given Medium Edge

Go Insphere Radius of Hexakis Octahedron = ((sqrt((402+(195*sqrt(2)))/194))/2)*((14*Medium Edge of Hexakis Octahedron)/(3*(1+(2*sqrt(2)))))

Insphere Radius of Hexakis Octahedron given Short Edge

Go Insphere Radius of Hexakis Octahedron = ((sqrt((402+(195*sqrt(2)))/194))/2)*((14*Short Edge of Hexakis Octahedron)/(10-sqrt(2)))

Insphere Radius of Hexakis Octahedron

Go Insphere Radius of Hexakis Octahedron = (Long Edge of Hexakis Octahedron/2)*(sqrt((402+(195*sqrt(2)))/194))

Insphere Radius of Hexakis Octahedron Formula

Insphere Radius of Hexakis Octahedron = (Long Edge of Hexakis Octahedron/2)*(sqrt((402+(195*sqrt(2)))/194))
r_i = (l_e(Long)/2)*(sqrt((402+(195*sqrt(2)))/194))

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 Insphere Radius of Hexakis Octahedron?

Insphere Radius of Hexakis Octahedron calculator uses Insphere Radius of Hexakis Octahedron = (Long Edge of Hexakis Octahedron/2)*(sqrt((402+(195*sqrt(2)))/194)) to calculate the Insphere Radius of Hexakis Octahedron, Insphere Radius of Hexakis Octahedron formula is defined as the radius of the sphere that is contained by the Hexakis Octahedron in such a way that all the faces just touching the sphere. Insphere Radius of Hexakis Octahedron is denoted by r_i symbol.

How to calculate Insphere Radius of Hexakis Octahedron using this online calculator? To use this online calculator for Insphere Radius of Hexakis Octahedron, enter Long Edge of Hexakis Octahedron (l_e(Long)) and hit the calculate button. Here is how the Insphere Radius of Hexakis Octahedron calculation can be explained with given input values -> 18.69136 = (20/2)*(sqrt((402+(195*sqrt(2)))/194)).

FAQ

What is Insphere Radius of Hexakis Octahedron?

Insphere Radius of Hexakis Octahedron formula is defined as the radius of the sphere that is contained by the Hexakis Octahedron in such a way that all the faces just touching the sphere and is represented as r_i = (l_e(Long)/2)*(sqrt((402+(195*sqrt(2)))/194)) or Insphere Radius of Hexakis Octahedron = (Long Edge of Hexakis Octahedron/2)*(sqrt((402+(195*sqrt(2)))/194)). 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 Insphere Radius of Hexakis Octahedron?

Insphere Radius of Hexakis Octahedron formula is defined as the radius of the sphere that is contained by the Hexakis Octahedron in such a way that all the faces just touching the sphere is calculated using Insphere Radius of Hexakis Octahedron = (Long Edge of Hexakis Octahedron/2)*(sqrt((402+(195*sqrt(2)))/194)). To calculate Insphere 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 Insphere Radius of Hexakis Octahedron?

In this formula, Insphere 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 -

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

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