Long 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]

+10%

-10%

✖Long Edge of Hexakis Octahedron is the length of the long edge of any of the congruent triangular faces of the Hexakis Octahedron.ⓘ Long Edge of Hexakis Octahedron given Midsphere Radius [l_e(Long)]

⎘ Copy

👎

Formula

✖

Long Edge of Hexakis Octahedron given Midsphere Radius

Formula

`"l"_{"e(Long)"} = (4*"r"_{"m"})/(1+(2*sqrt(2)))`

Example

`"19.85149m"=(4*"19m")/(1+(2*sqrt(2)))`

Calculator

LaTeX

Reset

👍

Download 3D Geometry Formula PDF

Long Edge of Hexakis Octahedron given Midsphere Radius Solution

STEP 0: Pre-Calculation Summary

Formula Used

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

Long Edge of Hexakis Octahedron - (Measured in Meter) - Long Edge of Hexakis Octahedron is the length of the long 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(Long) = (4*r_m)/(1+(2*sqrt(2))) --> (4*19)/(1+(2*sqrt(2)))

Evaluating ... ...

l_e(Long) = 19.8514944972443

STEP 3: Convert Result to Output's Unit

19.8514944972443 Meter --> No Conversion Required

FINAL ANSWER

19.8514944972443 ≈ 19.85149 Meter <-- Long Edge of Hexakis Octahedron

(Calculation completed in 00.004 seconds)

You are here -

Home » Math » Geometry » 3D Geometry » CatalanSolids » Hexakis Octahedron » Edges of Hexakis Octahedron » Long Edge of Hexakis Octahedron » Long Edge of Hexakis Octahedron given Midsphere Radius

Credits

Created by Shweta Patil

Walchand College of Engineering (WCE), Sangli

Shweta Patil has created this Calculator and 2500+ more calculators!

Verified by Mona Gladys

St Joseph's College (SJC), Bengaluru

Mona Gladys has verified this Calculator and 1800+ more calculators!

< 8 Long Edge of Hexakis Octahedron Calculators

Long Edge of Hexakis Octahedron given Surface to Volume Ratio

Go Long Edge of Hexakis Octahedron = (12*sqrt(543+(176*sqrt(2))))/ (Surface to Volume Ratio of Hexakis Octahedron*(sqrt(6*(986+(607*sqrt(2))))))

Long Edge of Hexakis Octahedron given Total Surface Area

Go Long Edge of Hexakis Octahedron = sqrt((7*Total Surface Area of Hexakis Octahedron)/(3*sqrt(543+(176*sqrt(2)))))

Long Edge of Hexakis Octahedron given Truncated Cuboctahedron Edge

Go Long Edge of Hexakis Octahedron = (2/7)*(sqrt(60+(6*sqrt(2))))*Truncated Cuboctahedron Edge of Hexakis Octahedron

Long Edge of Hexakis Octahedron given Insphere Radius

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

Long Edge of Hexakis Octahedron given Volume

Go Long Edge of Hexakis Octahedron = (((28*Volume of Hexakis Octahedron)/(sqrt(6*(986+(607*sqrt(2))))))^(1/3))

Long Edge of Hexakis Octahedron given Midsphere Radius

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

Long Edge of Hexakis Octahedron given Medium Edge

Go Long Edge of Hexakis Octahedron = (14/3)*(Medium Edge of Hexakis Octahedron/(1+(2*sqrt(2))))

Long Edge of Hexakis Octahedron given Short Edge

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

Long Edge of Hexakis Octahedron given Midsphere Radius Formula

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

Long Edge of Hexakis Octahedron given Midsphere Radius calculator uses Long Edge of Hexakis Octahedron = (4*Midsphere Radius of Hexakis Octahedron)/(1+(2*sqrt(2))) to calculate the Long Edge of Hexakis Octahedron, Long Edge of Hexakis Octahedron given Midsphere Radius formula is defined as the length of the long edge of any of the congruent triangular faces of the Hexakis Octahedron, calculated using midsphere radius of Hexakis Octahedron. Long Edge of Hexakis Octahedron is denoted by l_e(Long) symbol.

How to calculate Long Edge of Hexakis Octahedron given Midsphere Radius using this online calculator? To use this online calculator for Long Edge of Hexakis Octahedron given Midsphere Radius, enter Midsphere Radius of Hexakis Octahedron (r_m) and hit the calculate button. Here is how the Long Edge of Hexakis Octahedron given Midsphere Radius calculation can be explained with given input values -> 19.85149 = (4*19)/(1+(2*sqrt(2))).

FAQ

What is Long Edge of Hexakis Octahedron given Midsphere Radius?

Long Edge of Hexakis Octahedron given Midsphere Radius formula is defined as the length of the long 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(Long) = (4*r_m)/(1+(2*sqrt(2))) or Long Edge of Hexakis Octahedron = (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 Long Edge of Hexakis Octahedron given Midsphere Radius?

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

In this formula, Long Edge of Hexakis Octahedron uses Midsphere Radius of Hexakis Octahedron. We can use 7 other way(s) to calculate the same, which is/are as follows -

Long Edge of Hexakis Octahedron = (2/7)*(sqrt(60+(6*sqrt(2))))*Truncated Cuboctahedron Edge of Hexakis Octahedron
Long Edge of Hexakis Octahedron = (14/3)*(Medium Edge of Hexakis Octahedron/(1+(2*sqrt(2))))
Long Edge of Hexakis Octahedron = (14*Short Edge of Hexakis Octahedron)/(10-sqrt(2))
Long Edge of Hexakis Octahedron = sqrt((7*Total Surface Area of Hexakis Octahedron)/(3*sqrt(543+(176*sqrt(2)))))
Long Edge of Hexakis Octahedron = (((28*Volume of Hexakis Octahedron)/(sqrt(6*(986+(607*sqrt(2))))))^(1/3))
Long Edge of Hexakis Octahedron = (2*Insphere Radius of Hexakis Octahedron)/(sqrt((402+(195*sqrt(2)))/194))
Long Edge of Hexakis Octahedron = (12*sqrt(543+(176*sqrt(2))))/ (Surface to Volume Ratio of Hexakis Octahedron*(sqrt(6*(986+(607*sqrt(2))))))

Home

FREE PDFs

🔍 Search