Midsphere Radius of Hexakis Octahedron given Insphere Radius Calculator

✖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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✖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 given Insphere Radius [r_m]

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Midsphere Radius of Hexakis Octahedron given Insphere Radius Solution

STEP 0: Pre-Calculation Summary

Formula Used

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

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.
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.

STEP 1: Convert Input(s) to Base Unit

Insphere Radius of Hexakis Octahedron: 18 Meter --> 18 Meter No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

r_m = ((1+(2*sqrt(2)))/4)*((2*r_i)/(sqrt((402+(195*sqrt(2)))/194))) --> ((1+(2*sqrt(2)))/4)*((2*18)/(sqrt((402+(195*sqrt(2)))/194)))

Evaluating ... ...

r_m = 18.4341051807764

STEP 3: Convert Result to Output's Unit

18.4341051807764 Meter --> No Conversion Required

FINAL ANSWER

18.4341051807764 ≈ 18.43411 Meter <-- Midsphere Radius of Hexakis Octahedron

(Calculation completed in 00.004 seconds)

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< Midsphere Radius of Hexakis Octahedron Calculators

Midsphere Radius of Hexakis Octahedron given Total Surface Area

LaTeX 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 Short Edge

LaTeX 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

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

Midsphere Radius of Hexakis Octahedron given Medium Edge

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

Midsphere Radius of Hexakis Octahedron given Insphere Radius Formula

LaTeX Go

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 given Insphere Radius?

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

How to calculate Midsphere Radius of Hexakis Octahedron given Insphere Radius using this online calculator? To use this online calculator for Midsphere Radius of Hexakis Octahedron given Insphere Radius, enter Insphere Radius of Hexakis Octahedron (r_i) and hit the calculate button. Here is how the Midsphere Radius of Hexakis Octahedron given Insphere Radius calculation can be explained with given input values -> 18.43411 = ((1+(2*sqrt(2)))/4)*((2*18)/(sqrt((402+(195*sqrt(2)))/194))).

FAQ

What is Midsphere Radius of Hexakis Octahedron given Insphere Radius?

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

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

Midsphere Radius of Hexakis Octahedron given Insphere Radius 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, calculated using the insphere radius of Hexakis Octahedron is calculated using Midsphere Radius of Hexakis Octahedron = ((1+(2*sqrt(2)))/4)*((2*Insphere Radius of Hexakis Octahedron)/(sqrt((402+(195*sqrt(2)))/194))). To calculate Midsphere Radius of Hexakis Octahedron given Insphere Radius, you need Insphere Radius of Hexakis Octahedron (r_i). With our tool, you need to enter the respective value for Insphere 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 Midsphere Radius of Hexakis Octahedron?

In this formula, Midsphere Radius of Hexakis Octahedron uses Insphere Radius of Hexakis Octahedron. We can use 3 other way(s) to calculate the same, which is/are as follows -

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

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