Short Edge of Deltoidal Hexecontahedron given Insphere Radius Calculator

✖Insphere Radius of Deltoidal Hexecontahedron is the radius of the sphere that is contained by the Deltoidal Hexecontahedron in such a way that all the faces just touch the sphere.ⓘ Insphere Radius of Deltoidal Hexecontahedron [r_i]

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✖Short Edge of Deltoidal Hexecontahedron is the length of shortest edge of the identical deltoidal faces of Deltoidal Hexecontahedron.ⓘ Short Edge of Deltoidal Hexecontahedron given Insphere Radius [l_e(Short)]

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Formula

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Short Edge of Deltoidal Hexecontahedron given Insphere Radius

Formula

`"l"_{"e(Short)"} = 3/22*(7-sqrt(5))*(2*"r"_{"i"})/(3*sqrt((135+(59*sqrt(5)))/205))`

Example

`"6.452108m"=3/22*(7-sqrt(5))*(2*"17m")/(3*sqrt((135+(59*sqrt(5)))/205))`

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Short Edge of Deltoidal Hexecontahedron given Insphere Radius Solution

STEP 0: Pre-Calculation Summary

Formula Used

Short Edge of Deltoidal Hexecontahedron = 3/22*(7-sqrt(5))*(2*Insphere Radius of Deltoidal Hexecontahedron)/(3*sqrt((135+(59*sqrt(5)))/205))
l_e(Short) = 3/22*(7-sqrt(5))*(2*r_i)/(3*sqrt((135+(59*sqrt(5)))/205))
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 Deltoidal Hexecontahedron - (Measured in Meter) - Short Edge of Deltoidal Hexecontahedron is the length of shortest edge of the identical deltoidal faces of Deltoidal Hexecontahedron.
Insphere Radius of Deltoidal Hexecontahedron - (Measured in Meter) - Insphere Radius of Deltoidal Hexecontahedron is the radius of the sphere that is contained by the Deltoidal Hexecontahedron in such a way that all the faces just touch the sphere.

STEP 1: Convert Input(s) to Base Unit

Insphere Radius of Deltoidal Hexecontahedron: 17 Meter --> 17 Meter No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

l_e(Short) = 3/22*(7-sqrt(5))*(2*r_i)/(3*sqrt((135+(59*sqrt(5)))/205)) --> 3/22*(7-sqrt(5))*(2*17)/(3*sqrt((135+(59*sqrt(5)))/205))

Evaluating ... ...

l_e(Short) = 6.45210828747493

STEP 3: Convert Result to Output's Unit

6.45210828747493 Meter --> No Conversion Required

FINAL ANSWER

6.45210828747493 ≈ 6.452108 Meter <-- Short Edge of Deltoidal Hexecontahedron

(Calculation completed in 00.020 seconds)

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Home » Math » Geometry » 3D Geometry » CatalanSolids » Deltoidal Hexecontahedron » Edges of Deltoidal Hexecontahedron » Short Edge of Deltoidal Hexecontahedron » Short Edge of Deltoidal Hexecontahedron given Insphere Radius

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< 8 Short Edge of Deltoidal Hexecontahedron Calculators

Short Edge of Deltoidal Hexecontahedron given Surface to Volume Ratio

Go Short Edge of Deltoidal Hexecontahedron = 3/22*(7-sqrt(5))*(9/45*sqrt(10*(157+(31*sqrt(5)))))/(SA:V of Deltoidal Hexecontahedron*sqrt((370+(164*sqrt(5)))/25))

Short Edge of Deltoidal Hexecontahedron given Total Surface Area

Go Short Edge of Deltoidal Hexecontahedron = 3/22*(7-sqrt(5))*sqrt((11*Total Surface Area of Deltoidal Hexecontahedron)/(9*sqrt(10*(157+(31*sqrt(5))))))

Short Edge of Deltoidal Hexecontahedron given NonSymmetry Diagonal

Go Short Edge of Deltoidal Hexecontahedron = 3/22*(7-sqrt(5))*(11*NonSymmetry Diagonal of Deltoidal Hexecontahedron)/sqrt((470+(156*sqrt(5)))/5)

Short Edge of Deltoidal Hexecontahedron given Volume

Go Short Edge of Deltoidal Hexecontahedron = 3/22*(7-sqrt(5))*((11*Volume of Deltoidal Hexecontahedron)/(45*sqrt((370+(164*sqrt(5)))/25)))^(1/3)

Short Edge of Deltoidal Hexecontahedron given Insphere Radius

Go Short Edge of Deltoidal Hexecontahedron = 3/22*(7-sqrt(5))*(2*Insphere Radius of Deltoidal Hexecontahedron)/(3*sqrt((135+(59*sqrt(5)))/205))

Short Edge of Deltoidal Hexecontahedron given Symmetry Diagonal

Go Short Edge of Deltoidal Hexecontahedron = 3/22*(7-sqrt(5))*Symmetry Diagonal of Deltoidal Hexecontahedron/(3*sqrt((5-sqrt(5))/20))

Short Edge of Deltoidal Hexecontahedron given Midsphere Radius

Go Short Edge of Deltoidal Hexecontahedron = 3/22*(7-sqrt(5))*(20*Midsphere Radius of Deltoidal Hexecontahedron)/(3*(5+(3*sqrt(5))))

Short Edge of Deltoidal Hexecontahedron

Go Short Edge of Deltoidal Hexecontahedron = 3/22*(7-sqrt(5))*Long Edge of Deltoidal Hexecontahedron

Short Edge of Deltoidal Hexecontahedron given Insphere Radius Formula

What is Deltoidal Hexecontahedron?

A Deltoidal Hexecontahedron is a polyhedron with deltoid (kite) faces, those have two angles with 86.97°, one angle with 118.3° and one with 67.8°. It has twenty vertices with three edges, thirty vertices with four edges and twelve vertices with five edges. In total, it has 60 faces, 120 edges, 62 vertices.

How to Calculate Short Edge of Deltoidal Hexecontahedron given Insphere Radius?

Short Edge of Deltoidal Hexecontahedron given Insphere Radius calculator uses Short Edge of Deltoidal Hexecontahedron = 3/22*(7-sqrt(5))*(2*Insphere Radius of Deltoidal Hexecontahedron)/(3*sqrt((135+(59*sqrt(5)))/205)) to calculate the Short Edge of Deltoidal Hexecontahedron, Short Edge of Deltoidal Hexecontahedron given Insphere Radius formula is defined as the length of the shortest edge of the identical deltoidal faces of Deltoidal Hexecontahedron, calculated using insphere radius of Deltoidal Hexecontahedron. Short Edge of Deltoidal Hexecontahedron is denoted by l_e(Short) symbol.

How to calculate Short Edge of Deltoidal Hexecontahedron given Insphere Radius using this online calculator? To use this online calculator for Short Edge of Deltoidal Hexecontahedron given Insphere Radius, enter Insphere Radius of Deltoidal Hexecontahedron (r_i) and hit the calculate button. Here is how the Short Edge of Deltoidal Hexecontahedron given Insphere Radius calculation can be explained with given input values -> 6.452108 = 3/22*(7-sqrt(5))*(2*17)/(3*sqrt((135+(59*sqrt(5)))/205)).

FAQ

What is Short Edge of Deltoidal Hexecontahedron given Insphere Radius?

Short Edge of Deltoidal Hexecontahedron given Insphere Radius formula is defined as the length of the shortest edge of the identical deltoidal faces of Deltoidal Hexecontahedron, calculated using insphere radius of Deltoidal Hexecontahedron and is represented as l_e(Short) = 3/22*(7-sqrt(5))*(2*r_i)/(3*sqrt((135+(59*sqrt(5)))/205)) or Short Edge of Deltoidal Hexecontahedron = 3/22*(7-sqrt(5))*(2*Insphere Radius of Deltoidal Hexecontahedron)/(3*sqrt((135+(59*sqrt(5)))/205)). Insphere Radius of Deltoidal Hexecontahedron is the radius of the sphere that is contained by the Deltoidal Hexecontahedron in such a way that all the faces just touch the sphere.

How to calculate Short Edge of Deltoidal Hexecontahedron given Insphere Radius?

Short Edge of Deltoidal Hexecontahedron given Insphere Radius formula is defined as the length of the shortest edge of the identical deltoidal faces of Deltoidal Hexecontahedron, calculated using insphere radius of Deltoidal Hexecontahedron is calculated using Short Edge of Deltoidal Hexecontahedron = 3/22*(7-sqrt(5))*(2*Insphere Radius of Deltoidal Hexecontahedron)/(3*sqrt((135+(59*sqrt(5)))/205)). To calculate Short Edge of Deltoidal Hexecontahedron given Insphere Radius, you need Insphere Radius of Deltoidal Hexecontahedron (r_i). With our tool, you need to enter the respective value for Insphere Radius of Deltoidal Hexecontahedron 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 Deltoidal Hexecontahedron?

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

Short Edge of Deltoidal Hexecontahedron = 3/22*(7-sqrt(5))*Long Edge of Deltoidal Hexecontahedron
Short Edge of Deltoidal Hexecontahedron = 3/22*(7-sqrt(5))*Symmetry Diagonal of Deltoidal Hexecontahedron/(3*sqrt((5-sqrt(5))/20))
Short Edge of Deltoidal Hexecontahedron = 3/22*(7-sqrt(5))*(11*NonSymmetry Diagonal of Deltoidal Hexecontahedron)/sqrt((470+(156*sqrt(5)))/5)
Short Edge of Deltoidal Hexecontahedron = 3/22*(7-sqrt(5))*sqrt((11*Total Surface Area of Deltoidal Hexecontahedron)/(9*sqrt(10*(157+(31*sqrt(5))))))
Short Edge of Deltoidal Hexecontahedron = 3/22*(7-sqrt(5))*((11*Volume of Deltoidal Hexecontahedron)/(45*sqrt((370+(164*sqrt(5)))/25)))^(1/3)
Short Edge of Deltoidal Hexecontahedron = 3/22*(7-sqrt(5))*(20*Midsphere Radius of Deltoidal Hexecontahedron)/(3*(5+(3*sqrt(5))))
Short Edge of Deltoidal Hexecontahedron = 3/22*(7-sqrt(5))*(9/45*sqrt(10*(157+(31*sqrt(5)))))/(SA:V of Deltoidal Hexecontahedron*sqrt((370+(164*sqrt(5)))/25))

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