Short Edge 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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✖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 given Insphere Radius [l_e(Short)]

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Short Edge of Hexakis Octahedron given Insphere Radius Solution

STEP 0: Pre-Calculation Summary

Formula Used

Short Edge of Hexakis Octahedron = ((2*Insphere Radius of Hexakis Octahedron)/(sqrt((402+(195*sqrt(2)))/194)))*sqrt((30-(3*sqrt(2)))/(60+(6*sqrt(2))))
l_e(Short) = ((2*r_i)/(sqrt((402+(195*sqrt(2)))/194)))*sqrt((30-(3*sqrt(2)))/(60+(6*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

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.
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

l_e(Short) = ((2*r_i)/(sqrt((402+(195*sqrt(2)))/194)))*sqrt((30-(3*sqrt(2)))/(60+(6*sqrt(2)))) --> ((2*18)/(sqrt((402+(195*sqrt(2)))/194)))*sqrt((30-(3*sqrt(2)))/(60+(6*sqrt(2))))

Evaluating ... ...

l_e(Short) = 11.8117355168701

STEP 3: Convert Result to Output's Unit

11.8117355168701 Meter --> No Conversion Required

FINAL ANSWER

11.8117355168701 ≈ 11.81174 Meter <-- Short Edge of Hexakis Octahedron

(Calculation completed in 00.006 seconds)

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< Short Edge of Hexakis Octahedron Calculators

Short Edge of Hexakis Octahedron given Total Surface Area

LaTeX Go Short Edge of Hexakis Octahedron = ((10-sqrt(2))/14)*(sqrt((7*Total Surface Area of Hexakis Octahedron)/(3*sqrt(543+(176*sqrt(2))))))

Short Edge of Hexakis Octahedron given Truncated Cuboctahedron Edge

LaTeX Go Short Edge of Hexakis Octahedron = (2/7)*(sqrt(30-(3*sqrt(2))))*Truncated Cuboctahedron Edge of Hexakis Octahedron

Short Edge of Hexakis Octahedron given Medium Edge

LaTeX Go Short Edge of Hexakis Octahedron = ((10-sqrt(2))/14)*(14/(3*(1+(2*sqrt(2)))))*Medium Edge of Hexakis Octahedron

Short Edge of Hexakis Octahedron

LaTeX Go Short Edge of Hexakis Octahedron = (1/14)*(10-sqrt(2))*Long Edge of Hexakis Octahedron

Short Edge 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 Short Edge of Hexakis Octahedron given Insphere Radius?

Short Edge of Hexakis Octahedron given Insphere Radius calculator uses Short Edge of Hexakis Octahedron = ((2*Insphere Radius of Hexakis Octahedron)/(sqrt((402+(195*sqrt(2)))/194)))*sqrt((30-(3*sqrt(2)))/(60+(6*sqrt(2)))) to calculate the Short Edge of Hexakis Octahedron, Short Edge of Hexakis Octahedron given Insphere Radius formula is defined as the length of the shortest edge of any of the congruent triangular faces of the Hexakis Octahedron, calculated using insphere radius of Hexakis Octahedron. Short Edge of Hexakis Octahedron is denoted by l_e(Short) symbol.

How to calculate Short Edge of Hexakis Octahedron given Insphere Radius using this online calculator? To use this online calculator for Short Edge of Hexakis Octahedron given Insphere Radius, enter Insphere Radius of Hexakis Octahedron (r_i) and hit the calculate button. Here is how the Short Edge of Hexakis Octahedron given Insphere Radius calculation can be explained with given input values -> 11.81174 = ((2*18)/(sqrt((402+(195*sqrt(2)))/194)))*sqrt((30-(3*sqrt(2)))/(60+(6*sqrt(2)))).

FAQ

What is Short Edge of Hexakis Octahedron given Insphere Radius?

Short Edge of Hexakis Octahedron given Insphere Radius formula is defined as the length of the shortest edge of any of the congruent triangular faces of the Hexakis Octahedron, calculated using insphere radius of Hexakis Octahedron and is represented as l_e(Short) = ((2*r_i)/(sqrt((402+(195*sqrt(2)))/194)))*sqrt((30-(3*sqrt(2)))/(60+(6*sqrt(2)))) or Short Edge of Hexakis Octahedron = ((2*Insphere Radius of Hexakis Octahedron)/(sqrt((402+(195*sqrt(2)))/194)))*sqrt((30-(3*sqrt(2)))/(60+(6*sqrt(2)))). 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 Short Edge of Hexakis Octahedron given Insphere Radius?

Short Edge of Hexakis Octahedron given Insphere Radius formula is defined as the length of the shortest edge of any of the congruent triangular faces of the Hexakis Octahedron, calculated using insphere radius of Hexakis Octahedron is calculated using Short Edge of Hexakis Octahedron = ((2*Insphere Radius of Hexakis Octahedron)/(sqrt((402+(195*sqrt(2)))/194)))*sqrt((30-(3*sqrt(2)))/(60+(6*sqrt(2)))). To calculate Short Edge 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 Short Edge of Hexakis Octahedron?

In this formula, Short Edge 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 -

Short Edge of Hexakis Octahedron = (2/7)*(sqrt(30-(3*sqrt(2))))*Truncated Cuboctahedron Edge of Hexakis Octahedron
Short Edge of Hexakis Octahedron = (1/14)*(10-sqrt(2))*Long Edge of Hexakis Octahedron
Short Edge of Hexakis Octahedron = ((10-sqrt(2))/14)*(14/(3*(1+(2*sqrt(2)))))*Medium Edge of Hexakis Octahedron

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