Short Edge 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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✖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 Midsphere Radius [l_e(Short)]

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Short Edge of Hexakis Octahedron given Midsphere Radius Solution

STEP 0: Pre-Calculation Summary

Formula Used

Short Edge of Hexakis Octahedron = ((10-sqrt(2))/14)*((4*Midsphere Radius of Hexakis Octahedron)/(1+(2*sqrt(2))))
l_e(Short) = ((10-sqrt(2))/14)*((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

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.
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

l_e(Short) = ((10-sqrt(2))/14)*((4*r_m)/(1+(2*sqrt(2)))) --> ((10-sqrt(2))/14)*((4*19)/(1+(2*sqrt(2))))

Evaluating ... ...

l_e(Short) = 12.1743351586475

STEP 3: Convert Result to Output's Unit

12.1743351586475 Meter --> No Conversion Required

FINAL ANSWER

12.1743351586475 ≈ 12.17434 Meter <-- Short Edge of Hexakis Octahedron

(Calculation completed in 00.020 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 Midsphere Radius Formula

LaTeX Go

Short Edge of Hexakis Octahedron = ((10-sqrt(2))/14)*((4*Midsphere Radius of Hexakis Octahedron)/(1+(2*sqrt(2))))
l_e(Short) = ((10-sqrt(2))/14)*((4*r_m)/(1+(2*sqrt(2))))

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 Midsphere Radius?

Short Edge of Hexakis Octahedron given Midsphere Radius calculator uses Short Edge of Hexakis Octahedron = ((10-sqrt(2))/14)*((4*Midsphere Radius of Hexakis Octahedron)/(1+(2*sqrt(2)))) to calculate the Short Edge of Hexakis Octahedron, Short Edge of Hexakis Octahedron given Midsphere Radius formula is defined as the length of the shortest edge of any of the congruent triangular faces of the Hexakis Octahedron, calculated using midsphere 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 Midsphere Radius using this online calculator? To use this online calculator for Short Edge of Hexakis Octahedron given Midsphere Radius, enter Midsphere Radius of Hexakis Octahedron (r_m) and hit the calculate button. Here is how the Short Edge of Hexakis Octahedron given Midsphere Radius calculation can be explained with given input values -> 12.17434 = ((10-sqrt(2))/14)*((4*19)/(1+(2*sqrt(2)))).

FAQ

What is Short Edge of Hexakis Octahedron given Midsphere Radius?

Short Edge of Hexakis Octahedron given Midsphere Radius formula is defined as the length of the shortest edge of any of the congruent triangular faces of the Hexakis Octahedron, calculated using midsphere radius of Hexakis Octahedron and is represented as l_e(Short) = ((10-sqrt(2))/14)*((4*r_m)/(1+(2*sqrt(2)))) or Short Edge of Hexakis Octahedron = ((10-sqrt(2))/14)*((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 Short Edge of Hexakis Octahedron given Midsphere Radius?

Short Edge of Hexakis Octahedron given Midsphere Radius formula is defined as the length of the shortest edge of any of the congruent triangular faces of the Hexakis Octahedron, calculated using midsphere radius of Hexakis Octahedron is calculated using Short Edge of Hexakis Octahedron = ((10-sqrt(2))/14)*((4*Midsphere Radius of Hexakis Octahedron)/(1+(2*sqrt(2)))). To calculate Short Edge 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 Short Edge of Hexakis Octahedron?

In this formula, Short Edge 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 -

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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