Insphere Radius of Hexakis Octahedron given Short Edge Calculator

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

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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 Short Edge [r_i]

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Insphere Radius of Hexakis Octahedron given Short Edge Solution

STEP 0: Pre-Calculation Summary

Formula Used

Insphere Radius of Hexakis Octahedron = ((sqrt((402+(195*sqrt(2)))/194))/2)*((14*Short Edge of Hexakis Octahedron)/(10-sqrt(2)))
r_i = ((sqrt((402+(195*sqrt(2)))/194))/2)*((14*l_e(Short))/(10-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.
Short Edge of Hexakis Octahedron - (Measured in Meter) - Short Edge of Hexakis Octahedron is the length of the shortest edge of any of the congruent triangular faces of the Hexakis Octahedron.

STEP 1: Convert Input(s) to Base Unit

Short Edge of Hexakis Octahedron: 12 Meter --> 12 Meter No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

r_i = ((sqrt((402+(195*sqrt(2)))/194))/2)*((14*l_e(Short))/(10-sqrt(2))) --> ((sqrt((402+(195*sqrt(2)))/194))/2)*((14*12)/(10-sqrt(2)))

Evaluating ... ...

r_i = 18.2868977798815

STEP 3: Convert Result to Output's Unit

18.2868977798815 Meter --> No Conversion Required

FINAL ANSWER

18.2868977798815 ≈ 18.2869 Meter <-- Insphere Radius of Hexakis Octahedron

(Calculation completed in 00.008 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 Short Edge 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 Insphere Radius of Hexakis Octahedron given Short Edge?

Insphere Radius of Hexakis Octahedron given Short Edge calculator uses Insphere Radius of Hexakis Octahedron = ((sqrt((402+(195*sqrt(2)))/194))/2)*((14*Short Edge of Hexakis Octahedron)/(10-sqrt(2))) to calculate the Insphere Radius of Hexakis Octahedron, Insphere Radius of Hexakis Octahedron given Short Edge 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 short edge of Hexakis Octahedron. Insphere Radius of Hexakis Octahedron is denoted by r_i symbol.

How to calculate Insphere Radius of Hexakis Octahedron given Short Edge using this online calculator? To use this online calculator for Insphere Radius of Hexakis Octahedron given Short Edge, enter Short Edge of Hexakis Octahedron (l_e(Short)) and hit the calculate button. Here is how the Insphere Radius of Hexakis Octahedron given Short Edge calculation can be explained with given input values -> 18.2869 = ((sqrt((402+(195*sqrt(2)))/194))/2)*((14*12)/(10-sqrt(2))).

FAQ

What is Insphere Radius of Hexakis Octahedron given Short Edge?

Insphere Radius of Hexakis Octahedron given Short Edge 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 short edge of Hexakis Octahedron and is represented as r_i = ((sqrt((402+(195*sqrt(2)))/194))/2)*((14*l_e(Short))/(10-sqrt(2))) or Insphere Radius of Hexakis Octahedron = ((sqrt((402+(195*sqrt(2)))/194))/2)*((14*Short Edge of Hexakis Octahedron)/(10-sqrt(2))). Short Edge of Hexakis Octahedron is the length of the shortest edge of any of the congruent triangular faces of the Hexakis Octahedron.

How to calculate Insphere Radius of Hexakis Octahedron given Short Edge?

Insphere Radius of Hexakis Octahedron given Short Edge 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 short edge of Hexakis Octahedron is calculated using Insphere Radius of Hexakis Octahedron = ((sqrt((402+(195*sqrt(2)))/194))/2)*((14*Short Edge of Hexakis Octahedron)/(10-sqrt(2))). To calculate Insphere Radius of Hexakis Octahedron given Short Edge, you need Short Edge of Hexakis Octahedron (l_e(Short)). With our tool, you need to enter the respective value for Short 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 Short Edge 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)*(sqrt((7*Total Surface Area of Hexakis Octahedron)/(3*sqrt(543+(176*sqrt(2))))))

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