Insphere Radius of Triakis Icosahedron given Midsphere Radius Calculator

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

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

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Insphere Radius of Triakis Icosahedron given Midsphere Radius Solution

STEP 0: Pre-Calculation Summary

Formula Used

Insphere Radius of Triakis Icosahedron = ((sqrt((10*(33+(13*sqrt(5))))/61))/4)*((4*Midsphere Radius of Triakis Icosahedron)/(1+sqrt(5)))
r_i = ((sqrt((10*(33+(13*sqrt(5))))/61))/4)*((4*r_m)/(1+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 Triakis Icosahedron - (Measured in Meter) - Insphere Radius of Triakis Icosahedron is the radius of the sphere that is contained by the Triakis Icosahedron in such a way that all the faces just touching the sphere.
Midsphere Radius of Triakis Icosahedron - (Measured in Meter) - Midsphere Radius of Triakis Icosahedron is the radius of the sphere for which all the edges of the Triakis Icosahedron become a tangent line on that sphere.

STEP 1: Convert Input(s) to Base Unit

Midsphere Radius of Triakis Icosahedron: 7 Meter --> 7 Meter No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

r_i = ((sqrt((10*(33+(13*sqrt(5))))/61))/4)*((4*r_m)/(1+sqrt(5))) --> ((sqrt((10*(33+(13*sqrt(5))))/61))/4)*((4*7)/(1+sqrt(5)))

Evaluating ... ...

r_i = 6.90005343496911

STEP 3: Convert Result to Output's Unit

6.90005343496911 Meter --> No Conversion Required

FINAL ANSWER

6.90005343496911 ≈ 6.900053 Meter <-- Insphere Radius of Triakis Icosahedron

(Calculation completed in 00.004 seconds)

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< Insphere Radius of Triakis Icosahedron Calculators

Insphere Radius of Triakis Icosahedron given Total Surface Area

LaTeX Go Insphere Radius of Triakis Icosahedron = ((sqrt((10*(33+(13*sqrt(5))))/61))/4)*(sqrt((11*Total Surface Area of Triakis Icosahedron)/(15*(sqrt(109-(30*sqrt(5)))))))

Insphere Radius of Triakis Icosahedron given Pyramidal Edge Length

LaTeX Go Insphere Radius of Triakis Icosahedron = ((sqrt((10*(33+(13*sqrt(5))))/61))/4)*((22*Pyramidal Edge Length of Triakis Icosahedron)/(15-sqrt(5)))

Insphere Radius of Triakis Icosahedron given Volume

LaTeX Go Insphere Radius of Triakis Icosahedron = ((sqrt((10*(33+(13*sqrt(5))))/61))/4)*(((44*Volume of Triakis Icosahedron)/(5*(5+(7*sqrt(5)))))^(1/3))

Insphere Radius of Triakis Icosahedron

LaTeX Go Insphere Radius of Triakis Icosahedron = ((sqrt((10*(33+(13*sqrt(5))))/61))/4)*Icosahedral Edge Length of Triakis Icosahedron

Insphere Radius of Triakis Icosahedron given Midsphere Radius Formula

LaTeX Go

What is Triakis Icosahedron?

The Triakis Icosahedron is a three-dimensional polyhedron created from the dual of the truncated dodecahedron. Because of this, it shares the same full icosahedral symmetry group as the dodecahedron and the truncated dodecahedron. It can also be constructed by adding short triangular pyramids onto the faces of an icosahedron. It has 60 faces, 90 edges, 32 vertices.

How to Calculate Insphere Radius of Triakis Icosahedron given Midsphere Radius?

Insphere Radius of Triakis Icosahedron given Midsphere Radius calculator uses Insphere Radius of Triakis Icosahedron = ((sqrt((10*(33+(13*sqrt(5))))/61))/4)*((4*Midsphere Radius of Triakis Icosahedron)/(1+sqrt(5))) to calculate the Insphere Radius of Triakis Icosahedron, Insphere Radius of Triakis Icosahedron given Midsphere Radius formula is defined as the radius of the sphere that is contained by the Triakis Icosahedron in such a way that all the faces just touching the sphere, calculated using midsphere radius of Triakis Icosahedron. Insphere Radius of Triakis Icosahedron is denoted by r_i symbol.

How to calculate Insphere Radius of Triakis Icosahedron given Midsphere Radius using this online calculator? To use this online calculator for Insphere Radius of Triakis Icosahedron given Midsphere Radius, enter Midsphere Radius of Triakis Icosahedron (r_m) and hit the calculate button. Here is how the Insphere Radius of Triakis Icosahedron given Midsphere Radius calculation can be explained with given input values -> 6.900053 = ((sqrt((10*(33+(13*sqrt(5))))/61))/4)*((4*7)/(1+sqrt(5))).

FAQ

What is Insphere Radius of Triakis Icosahedron given Midsphere Radius?

Insphere Radius of Triakis Icosahedron given Midsphere Radius formula is defined as the radius of the sphere that is contained by the Triakis Icosahedron in such a way that all the faces just touching the sphere, calculated using midsphere radius of Triakis Icosahedron and is represented as r_i = ((sqrt((10*(33+(13*sqrt(5))))/61))/4)*((4*r_m)/(1+sqrt(5))) or Insphere Radius of Triakis Icosahedron = ((sqrt((10*(33+(13*sqrt(5))))/61))/4)*((4*Midsphere Radius of Triakis Icosahedron)/(1+sqrt(5))). Midsphere Radius of Triakis Icosahedron is the radius of the sphere for which all the edges of the Triakis Icosahedron become a tangent line on that sphere.

How to calculate Insphere Radius of Triakis Icosahedron given Midsphere Radius?

Insphere Radius of Triakis Icosahedron given Midsphere Radius formula is defined as the radius of the sphere that is contained by the Triakis Icosahedron in such a way that all the faces just touching the sphere, calculated using midsphere radius of Triakis Icosahedron is calculated using Insphere Radius of Triakis Icosahedron = ((sqrt((10*(33+(13*sqrt(5))))/61))/4)*((4*Midsphere Radius of Triakis Icosahedron)/(1+sqrt(5))). To calculate Insphere Radius of Triakis Icosahedron given Midsphere Radius, you need Midsphere Radius of Triakis Icosahedron (r_m). With our tool, you need to enter the respective value for Midsphere Radius of Triakis 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 Triakis Icosahedron?

In this formula, Insphere Radius of Triakis Icosahedron uses Midsphere Radius of Triakis Icosahedron. We can use 3 other way(s) to calculate the same, which is/are as follows -

Insphere Radius of Triakis Icosahedron = ((sqrt((10*(33+(13*sqrt(5))))/61))/4)*Icosahedral Edge Length of Triakis Icosahedron
Insphere Radius of Triakis Icosahedron = ((sqrt((10*(33+(13*sqrt(5))))/61))/4)*((22*Pyramidal Edge Length of Triakis Icosahedron)/(15-sqrt(5)))
Insphere Radius of Triakis Icosahedron = ((sqrt((10*(33+(13*sqrt(5))))/61))/4)*(sqrt((11*Total Surface Area of Triakis Icosahedron)/(15*(sqrt(109-(30*sqrt(5)))))))

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