Insphere Radius 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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✖Insphere Radius of Hexakis Icosahedron is defined as the radius of the sphere that is contained by the Hexakis Icosahedron in such a way that all the faces just touching the sphere.ⓘ Insphere Radius of Hexakis Icosahedron given Midsphere Radius [r_i]

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Formula

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Insphere Radius of Hexakis Icosahedron given Midsphere Radius

Formula

`"r"_{"i"} = ((sqrt((15/241)*(275+(119*sqrt(5)))))/4)*((8*"r"_{"m"})/(5+(3*sqrt(5))))`

Example

`"14.86975m"=((sqrt((15/241)*(275+(119*sqrt(5)))))/4)*((8*"15m")/(5+(3*sqrt(5))))`

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Insphere Radius of Hexakis Icosahedron given Midsphere Radius Solution

STEP 0: Pre-Calculation Summary

Formula Used

Insphere Radius of Hexakis Icosahedron = ((sqrt((15/241)*(275+(119*sqrt(5)))))/4)*((8*Midsphere Radius of Hexakis Icosahedron)/(5+(3*sqrt(5))))
r_i = ((sqrt((15/241)*(275+(119*sqrt(5)))))/4)*((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

Insphere Radius of Hexakis Icosahedron - (Measured in Meter) - Insphere Radius of Hexakis Icosahedron is defined as the radius of the sphere that is contained by the Hexakis Icosahedron in such a way that all the faces just touching the sphere.
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

r_i = ((sqrt((15/241)*(275+(119*sqrt(5)))))/4)*((8*r_m)/(5+(3*sqrt(5)))) --> ((sqrt((15/241)*(275+(119*sqrt(5)))))/4)*((8*15)/(5+(3*sqrt(5))))

Evaluating ... ...

r_i = 14.8697503431159

STEP 3: Convert Result to Output's Unit

14.8697503431159 Meter --> No Conversion Required

FINAL ANSWER

14.8697503431159 ≈ 14.86975 Meter <-- Insphere Radius of Hexakis Icosahedron

(Calculation completed in 00.004 seconds)

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< 8 Insphere Radius of Hexakis Icosahedron Calculators

Insphere Radius of Hexakis Icosahedron given Surface to Volume Ratio

Go Insphere Radius of Hexakis Icosahedron = ((sqrt((15/241)*(275+(119*sqrt(5)))))/4)*((6/5)/Surface to Volume Ratio of Hexakis Icosahedron)*(sqrt((10*(417+(107*sqrt(5))))/(6*(185+(82*sqrt(5))))))

Insphere Radius of Hexakis Icosahedron given Total Surface Area

Go Insphere Radius of Hexakis Icosahedron = ((sqrt((15/241)*(275+(119*sqrt(5)))))/4)*(sqrt((44*Total Surface Area of Hexakis Icosahedron)/(15*(sqrt(10*(417+(107*sqrt(5))))))))

Insphere Radius of Hexakis Icosahedron given Volume

Go Insphere Radius of Hexakis Icosahedron = ((sqrt((15/241)*(275+(119*sqrt(5)))))/4)*(((88*Volume of Hexakis Icosahedron)/(25*(sqrt(6*(185+(82*sqrt(5)))))))^(1/3))

Insphere Radius of Hexakis Icosahedron given Truncated Icosidodecahedron Edge

Go Insphere Radius of Hexakis Icosahedron = ((sqrt((15/241)*(275+(119*sqrt(5)))))/4)*(2/5)*(Truncated Edge of Hexakis Icosahedron)*(sqrt(15*(5-sqrt(5))))

Insphere Radius of Hexakis Icosahedron given Midsphere Radius

Go Insphere Radius of Hexakis Icosahedron = ((sqrt((15/241)*(275+(119*sqrt(5)))))/4)*((8*Midsphere Radius of Hexakis Icosahedron)/(5+(3*sqrt(5))))

Insphere Radius of Hexakis Icosahedron given Medium Edge

Go Insphere Radius of Hexakis Icosahedron = ((sqrt((15/241)*(275+(119*sqrt(5)))))/4)*((22*Medium Edge of Hexakis Icosahedron)/(3*(4+sqrt(5))))

Insphere Radius of Hexakis Icosahedron given Short Edge

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

Insphere Radius of Hexakis Icosahedron

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

Insphere Radius of Hexakis Icosahedron given Midsphere Radius Formula

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 Insphere Radius of Hexakis Icosahedron given Midsphere Radius?

Insphere Radius of Hexakis Icosahedron given Midsphere Radius calculator uses Insphere Radius of Hexakis Icosahedron = ((sqrt((15/241)*(275+(119*sqrt(5)))))/4)*((8*Midsphere Radius of Hexakis Icosahedron)/(5+(3*sqrt(5)))) to calculate the Insphere Radius of Hexakis Icosahedron, Insphere Radius of Hexakis Icosahedron given Midsphere Radius formula is defined as the radius of the sphere that is contained by the Hexakis Icosahedron in such a way that all the faces just touch the sphere, calculated using midsphere radius of Hexakis Icosahedron. Insphere Radius of Hexakis Icosahedron is denoted by r_i symbol.

How to calculate Insphere Radius of Hexakis Icosahedron given Midsphere Radius using this online calculator? To use this online calculator for Insphere Radius of Hexakis Icosahedron given Midsphere Radius, enter Midsphere Radius of Hexakis Icosahedron (r_m) and hit the calculate button. Here is how the Insphere Radius of Hexakis Icosahedron given Midsphere Radius calculation can be explained with given input values -> 14.86975 = ((sqrt((15/241)*(275+(119*sqrt(5)))))/4)*((8*15)/(5+(3*sqrt(5)))).

FAQ

What is Insphere Radius of Hexakis Icosahedron given Midsphere Radius?

Insphere Radius of Hexakis Icosahedron given Midsphere Radius formula is defined as the radius of the sphere that is contained by the Hexakis Icosahedron in such a way that all the faces just touch the sphere, calculated using midsphere radius of Hexakis Icosahedron and is represented as r_i = ((sqrt((15/241)*(275+(119*sqrt(5)))))/4)*((8*r_m)/(5+(3*sqrt(5)))) or Insphere Radius of Hexakis Icosahedron = ((sqrt((15/241)*(275+(119*sqrt(5)))))/4)*((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 Insphere Radius of Hexakis Icosahedron given Midsphere Radius?

Insphere Radius of Hexakis Icosahedron given Midsphere Radius formula is defined as the radius of the sphere that is contained by the Hexakis Icosahedron in such a way that all the faces just touch the sphere, calculated using midsphere radius of Hexakis Icosahedron is calculated using Insphere Radius of Hexakis Icosahedron = ((sqrt((15/241)*(275+(119*sqrt(5)))))/4)*((8*Midsphere Radius of Hexakis Icosahedron)/(5+(3*sqrt(5)))). To calculate Insphere Radius 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 Insphere Radius of Hexakis Icosahedron?

In this formula, Insphere Radius 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 -

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

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