Short Edge of Hexakis Icosahedron given Midsphere Radius Calculator

✖Midsphere Radius of Hexakis Icosahedron is defined as the radius of the sphere for which all the edges of the Hexakis Icosahedron become a tangent line on that sphere.ⓘ Midsphere Radius of Hexakis Icosahedron [r_m]

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✖Short Edge of Hexakis Icosahedron is the length of the shortest edge that connects two adjacent vertices of the Hexakis Icosahedron.ⓘ Short Edge of Hexakis Icosahedron given Midsphere Radius [l_e(Short)]

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Formula

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Short Edge of Hexakis Icosahedron given Midsphere Radius

Formula

`"l"_{"e(Short)"} = (5/44)*(7-sqrt(5))*((8*"r"_{"m"})/(5+(3*sqrt(5))))`

Example

`"5.548478m"=(5/44)*(7-sqrt(5))*((8*"15m")/(5+(3*sqrt(5))))`

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Short Edge of Hexakis Icosahedron given Midsphere Radius Solution

STEP 0: Pre-Calculation Summary

Formula Used

Short Edge of Hexakis Icosahedron = (5/44)*(7-sqrt(5))*((8*Midsphere Radius of Hexakis Icosahedron)/(5+(3*sqrt(5))))
l_e(Short) = (5/44)*(7-sqrt(5))*((8*r_m)/(5+(3*sqrt(5))))
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 Icosahedron - (Measured in Meter) - Short Edge of Hexakis Icosahedron is the length of the shortest edge that connects two adjacent vertices of the Hexakis Icosahedron.
Midsphere Radius of Hexakis Icosahedron - (Measured in Meter) - Midsphere Radius of Hexakis Icosahedron is defined as the radius of the sphere for which all the edges of the Hexakis Icosahedron become a tangent line on that sphere.

STEP 1: Convert Input(s) to Base Unit

Midsphere Radius of Hexakis Icosahedron: 15 Meter --> 15 Meter No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

l_e(Short) = (5/44)*(7-sqrt(5))*((8*r_m)/(5+(3*sqrt(5)))) --> (5/44)*(7-sqrt(5))*((8*15)/(5+(3*sqrt(5))))

Evaluating ... ...

l_e(Short) = 5.54847778295082

STEP 3: Convert Result to Output's Unit

5.54847778295082 Meter --> No Conversion Required

FINAL ANSWER

5.54847778295082 ≈ 5.548478 Meter <-- Short Edge of Hexakis Icosahedron

(Calculation completed in 00.004 seconds)

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< 8 Short Edge of Hexakis Icosahedron Calculators

Short Edge of Hexakis Icosahedron given Surface to Volume Ratio

Go Short Edge of Hexakis Icosahedron = (5/44)*(7-sqrt(5))*(((6/5)*(sqrt(10*(417+(107*sqrt(5))))))/(Surface to Volume Ratio of Hexakis Icosahedron*(sqrt(6*(185+(82*sqrt(5)))))))

Short Edge of Hexakis Icosahedron given Total Surface Area

Go Short Edge of Hexakis Icosahedron = (5/44)*(7-sqrt(5))*(sqrt((44*Total Surface Area of Hexakis Icosahedron)/(15*(sqrt(10*(417+(107*sqrt(5))))))))

Short Edge of Hexakis Icosahedron given Insphere Radius

Go Short Edge of Hexakis Icosahedron = (5/44)*(7-sqrt(5))*((4*Insphere Radius of Hexakis Icosahedron)/(sqrt((15/241)*(275+(119*sqrt(5))))))

Short Edge of Hexakis Icosahedron given Volume

Go Short Edge of Hexakis Icosahedron = (5/44)*(7-sqrt(5))*(((88*Volume of Hexakis Icosahedron)/(25*(sqrt(6*(185+(82*sqrt(5)))))))^(1/3))

Short Edge of Hexakis Icosahedron given Truncated Icosidodecahedron Edge

Go Short Edge of Hexakis Icosahedron = (5/44)*(7-sqrt(5))*(2/5)*(sqrt(15*(5-sqrt(5))))*Truncated Edge of Hexakis Icosahedron

Short Edge of Hexakis Icosahedron given Midsphere Radius

Go Short Edge of Hexakis Icosahedron = (5/44)*(7-sqrt(5))*((8*Midsphere Radius of Hexakis Icosahedron)/(5+(3*sqrt(5))))

Short Edge of Hexakis Icosahedron given Medium Edge

Go Short Edge of Hexakis Icosahedron = (5/44)*(7-sqrt(5))*((22*Medium Edge of Hexakis Icosahedron)/(3*(4+sqrt(5))))

Short Edge of Hexakis Icosahedron

Go Short Edge of Hexakis Icosahedron = (5/44)*(7-sqrt(5))*Long Edge of Hexakis Icosahedron

Short Edge of Hexakis Icosahedron given Midsphere Radius Formula

Short Edge of Hexakis Icosahedron = (5/44)*(7-sqrt(5))*((8*Midsphere Radius of Hexakis Icosahedron)/(5+(3*sqrt(5))))
l_e(Short) = (5/44)*(7-sqrt(5))*((8*r_m)/(5+(3*sqrt(5))))

What is Hexakis Icosahedron?

A Hexakis Icosahedron is a polyhedron with identical, but irregular triangle faces. It has thirty vertices with four edges, twenty vertices with six edges and twelve vertices with ten edges.
It has 120 faces, 180 edges, 62 vertices.

How to Calculate Short Edge of Hexakis Icosahedron given Midsphere Radius?

Short Edge of Hexakis Icosahedron given Midsphere Radius calculator uses Short Edge of Hexakis Icosahedron = (5/44)*(7-sqrt(5))*((8*Midsphere Radius of Hexakis Icosahedron)/(5+(3*sqrt(5)))) to calculate the Short Edge of Hexakis Icosahedron, Short Edge of Hexakis Icosahedron given Midsphere Radius formula is defined as the length of the shortest edge that connects two adjacent vertices of the Hexakis Icosahedron, calculated using midsphere radius of Hexakis Icosahedron. Short Edge of Hexakis Icosahedron is denoted by l_e(Short) symbol.

How to calculate Short Edge of Hexakis Icosahedron given Midsphere Radius using this online calculator? To use this online calculator for Short Edge of Hexakis Icosahedron given Midsphere Radius, enter Midsphere Radius of Hexakis Icosahedron (r_m) and hit the calculate button. Here is how the Short Edge of Hexakis Icosahedron given Midsphere Radius calculation can be explained with given input values -> 5.548478 = (5/44)*(7-sqrt(5))*((8*15)/(5+(3*sqrt(5)))).

FAQ

What is Short Edge of Hexakis Icosahedron given Midsphere Radius?

Short Edge of Hexakis Icosahedron given Midsphere Radius formula is defined as the length of the shortest edge that connects two adjacent vertices of the Hexakis Icosahedron, calculated using midsphere radius of Hexakis Icosahedron and is represented as l_e(Short) = (5/44)*(7-sqrt(5))*((8*r_m)/(5+(3*sqrt(5)))) or Short Edge of Hexakis Icosahedron = (5/44)*(7-sqrt(5))*((8*Midsphere Radius of Hexakis Icosahedron)/(5+(3*sqrt(5)))). Midsphere Radius of Hexakis Icosahedron is defined as the radius of the sphere for which all the edges of the Hexakis Icosahedron become a tangent line on that sphere.

How to calculate Short Edge of Hexakis Icosahedron given Midsphere Radius?

Short Edge of Hexakis Icosahedron given Midsphere Radius formula is defined as the length of the shortest edge that connects two adjacent vertices of the Hexakis Icosahedron, calculated using midsphere radius of Hexakis Icosahedron is calculated using Short Edge of Hexakis Icosahedron = (5/44)*(7-sqrt(5))*((8*Midsphere Radius of Hexakis Icosahedron)/(5+(3*sqrt(5)))). To calculate Short Edge of Hexakis Icosahedron given Midsphere Radius, you need Midsphere Radius of Hexakis Icosahedron (r_m). With our tool, you need to enter the respective value for Midsphere Radius of Hexakis Icosahedron 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 Icosahedron?

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

Short Edge of Hexakis Icosahedron = (5/44)*(7-sqrt(5))*Long Edge of Hexakis Icosahedron
Short Edge of Hexakis Icosahedron = (5/44)*(7-sqrt(5))*((22*Medium Edge of Hexakis Icosahedron)/(3*(4+sqrt(5))))
Short Edge of Hexakis Icosahedron = (5/44)*(7-sqrt(5))*(2/5)*(sqrt(15*(5-sqrt(5))))*Truncated Edge of Hexakis Icosahedron
Short Edge of Hexakis Icosahedron = (5/44)*(7-sqrt(5))*(sqrt((44*Total Surface Area of Hexakis Icosahedron)/(15*(sqrt(10*(417+(107*sqrt(5))))))))
Short Edge of Hexakis Icosahedron = (5/44)*(7-sqrt(5))*(((88*Volume of Hexakis Icosahedron)/(25*(sqrt(6*(185+(82*sqrt(5)))))))^(1/3))
Short Edge of Hexakis Icosahedron = (5/44)*(7-sqrt(5))*((4*Insphere Radius of Hexakis Icosahedron)/(sqrt((15/241)*(275+(119*sqrt(5))))))
Short Edge of Hexakis Icosahedron = (5/44)*(7-sqrt(5))*(((6/5)*(sqrt(10*(417+(107*sqrt(5))))))/(Surface to Volume Ratio of Hexakis Icosahedron*(sqrt(6*(185+(82*sqrt(5)))))))

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