Insphere Radius of Hexakis Octahedron given Midsphere Radius Calculator

✖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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✖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 given Midsphere Radius [r_i]

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Insphere Radius of Hexakis Octahedron given Midsphere Radius Solution

STEP 0: Pre-Calculation Summary

Formula Used

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

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.
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.

STEP 1: Convert Input(s) to Base Unit

Midsphere Radius of Hexakis Octahedron: 19 Meter --> 19 Meter No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

r_i = ((sqrt((402+(195*sqrt(2)))/194))/2)*((4*r_m)/(1+(2*sqrt(2)))) --> ((sqrt((402+(195*sqrt(2)))/194))/2)*((4*19)/(1+(2*sqrt(2))))

Evaluating ... ...

r_i = 18.5525685486838

STEP 3: Convert Result to Output's Unit

18.5525685486838 Meter --> No Conversion Required

FINAL ANSWER

18.5525685486838 ≈ 18.55257 Meter <-- Insphere Radius of Hexakis Octahedron

(Calculation completed in 00.006 seconds)

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< Insphere Radius of Hexakis Octahedron Calculators

Insphere Radius of Hexakis Octahedron given Total Surface Area

LaTeX 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 Medium Edge

LaTeX 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

LaTeX 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

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

Insphere Radius of Hexakis Octahedron given Midsphere Radius Formula

LaTeX Go

What is Hexakis Octahedron?

In geometry, a Hexakis Octahedron , (also hexoctahedron, disdyakis dodecahedron , octakis cube, octakis hexahedron, kisrhombic dodecahedron), is a Catalan solid with 48 faces and the dual to the Archimedean truncated cuboctahedron. As such it is face-transitive but with irregular face polygons.

How to Calculate Insphere Radius of Hexakis Octahedron given Midsphere Radius?

Insphere Radius of Hexakis Octahedron given Midsphere Radius calculator uses Insphere Radius of Hexakis Octahedron = ((sqrt((402+(195*sqrt(2)))/194))/2)*((4*Midsphere Radius of Hexakis Octahedron)/(1+(2*sqrt(2)))) to calculate the Insphere Radius of Hexakis Octahedron, Insphere Radius of Hexakis Octahedron given Midsphere Radius 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, calculated using the midsphere radius of Hexakis Octahedron. Insphere Radius of Hexakis Octahedron is denoted by r_i symbol.

How to calculate Insphere Radius of Hexakis Octahedron given Midsphere Radius using this online calculator? To use this online calculator for Insphere Radius of Hexakis Octahedron given Midsphere Radius, enter Midsphere Radius of Hexakis Octahedron (r_m) and hit the calculate button. Here is how the Insphere Radius of Hexakis Octahedron given Midsphere Radius calculation can be explained with given input values -> 18.55257 = ((sqrt((402+(195*sqrt(2)))/194))/2)*((4*19)/(1+(2*sqrt(2)))).

FAQ

What is Insphere Radius of Hexakis Octahedron given Midsphere Radius?

Insphere Radius of Hexakis Octahedron given Midsphere Radius 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, calculated using the midsphere radius of Hexakis Octahedron and is represented as r_i = ((sqrt((402+(195*sqrt(2)))/194))/2)*((4*r_m)/(1+(2*sqrt(2)))) or Insphere Radius of Hexakis Octahedron = ((sqrt((402+(195*sqrt(2)))/194))/2)*((4*Midsphere Radius of Hexakis Octahedron)/(1+(2*sqrt(2)))). 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.

How to calculate Insphere Radius of Hexakis Octahedron given Midsphere Radius?

Insphere Radius of Hexakis Octahedron given Midsphere Radius 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, calculated using the midsphere radius of Hexakis Octahedron is calculated using Insphere Radius of Hexakis Octahedron = ((sqrt((402+(195*sqrt(2)))/194))/2)*((4*Midsphere Radius of Hexakis Octahedron)/(1+(2*sqrt(2)))). To calculate Insphere Radius of Hexakis Octahedron given Midsphere Radius, you need Midsphere Radius of Hexakis Octahedron (r_m). With our tool, you need to enter the respective value for Midsphere Radius 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 Midsphere Radius of Hexakis Octahedron. We can use 3 other way(s) to calculate the same, which is/are as follows -

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

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