Midsphere Radius of Hexakis Icosahedron given Short Edge Calculator

✖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 [l_e(Short)]

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✖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 given Short Edge [r_m]

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Formula

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Midsphere Radius of Hexakis Icosahedron given Short Edge

Formula

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

Example

`"13.51722m"=((5+(3*sqrt(5)))/8)*((44*"5m")/(5*(7-sqrt(5))))`

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Midsphere Radius of Hexakis Icosahedron given Short Edge Solution

STEP 0: Pre-Calculation Summary

Formula Used

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

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.
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.

STEP 1: Convert Input(s) to Base Unit

Short Edge of Hexakis Icosahedron: 5 Meter --> 5 Meter No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

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

Evaluating ... ...

r_m = 13.5172209268743

STEP 3: Convert Result to Output's Unit

13.5172209268743 Meter --> No Conversion Required

FINAL ANSWER

13.5172209268743 ≈ 13.51722 Meter <-- Midsphere Radius of Hexakis Icosahedron

(Calculation completed in 00.021 seconds)

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Created by Shweta Patil

Walchand College of Engineering (WCE), Sangli

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Indian Institute of Information Technology (IIIT), Bhopal

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< 8 Midsphere Radius of Hexakis Icosahedron Calculators

Midsphere Radius of Hexakis Icosahedron given Surface to Volume Ratio

Go Midsphere Radius of Hexakis Icosahedron = 1/8*(6/5*sqrt(10*(417+107*sqrt(5)))/(Surface to Volume Ratio of Hexakis Icosahedron*sqrt(6*(185+82*sqrt(5)))))*(5+3*sqrt(5))

Midsphere Radius of Hexakis Icosahedron given Total Surface Area

Go Midsphere Radius of Hexakis Icosahedron = 1/8*sqrt(44/15*Total Surface Area of Hexakis Icosahedron/sqrt(10*(417+107*sqrt(5))))*(5+3*sqrt(5))

Midsphere Radius of Hexakis Icosahedron given Insphere Radius

Go Midsphere Radius of Hexakis Icosahedron = 1/8*(4*Insphere Radius of Hexakis Icosahedron/sqrt(15/241*(275+119*sqrt(5))))*(5+3*sqrt(5))

Midsphere Radius of Hexakis Icosahedron given Truncated Icosidodecahedron Edge

Go Midsphere Radius of Hexakis Icosahedron = ((5+(3*sqrt(5)))/8)*(2/5)*(Truncated Edge of Hexakis Icosahedron)*(sqrt(15*(5-sqrt(5))))

Midsphere Radius of Hexakis Icosahedron given Volume

Go Midsphere Radius of Hexakis Icosahedron = 1/8*(88/25*Volume of Hexakis Icosahedron/sqrt(6*(185+82*sqrt(5))))^(1/3)*(5+3*sqrt(5))

Midsphere Radius of Hexakis Icosahedron given Medium Edge

Go Midsphere Radius of Hexakis Icosahedron = ((5+(3*sqrt(5)))/8)*((22*Medium Edge of Hexakis Icosahedron)/(3*(4+sqrt(5))))

Midsphere Radius of Hexakis Icosahedron given Short Edge

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

Midsphere Radius of Hexakis Icosahedron

Go Midsphere Radius of Hexakis Icosahedron = Long Edge of Hexakis Icosahedron/8*(5+3*sqrt(5))

Midsphere Radius of Hexakis Icosahedron given Short Edge Formula

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

Midsphere Radius of Hexakis Icosahedron given Short Edge calculator uses Midsphere Radius of Hexakis Icosahedron = ((5+(3*sqrt(5)))/8)*((44*Short Edge of Hexakis Icosahedron)/(5*(7-sqrt(5)))) to calculate the Midsphere Radius of Hexakis Icosahedron, Midsphere Radius of Hexakis Icosahedron given Short Edge formula is defined as the radius of the sphere for which all the edges of the Hexakis Icosahedron become a tangent line on that sphere, calculated using short edge of Hexakis Icosahedron. Midsphere Radius of Hexakis Icosahedron is denoted by r_m symbol.

How to calculate Midsphere Radius of Hexakis Icosahedron given Short Edge using this online calculator? To use this online calculator for Midsphere Radius of Hexakis Icosahedron given Short Edge, enter Short Edge of Hexakis Icosahedron (l_e(Short)) and hit the calculate button. Here is how the Midsphere Radius of Hexakis Icosahedron given Short Edge calculation can be explained with given input values -> 13.51722 = ((5+(3*sqrt(5)))/8)*((44*5)/(5*(7-sqrt(5)))).

FAQ

What is Midsphere Radius of Hexakis Icosahedron given Short Edge?

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

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

Midsphere Radius of Hexakis Icosahedron given Short Edge formula is defined as the radius of the sphere for which all the edges of the Hexakis Icosahedron become a tangent line on that sphere, calculated using short edge of Hexakis Icosahedron is calculated using Midsphere Radius of Hexakis Icosahedron = ((5+(3*sqrt(5)))/8)*((44*Short Edge of Hexakis Icosahedron)/(5*(7-sqrt(5)))). To calculate Midsphere Radius of Hexakis Icosahedron given Short Edge, you need Short Edge of Hexakis Icosahedron (l_e(Short)). With our tool, you need to enter the respective value for Short Edge 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 Midsphere Radius of Hexakis Icosahedron?

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

Midsphere Radius of Hexakis Icosahedron = ((5+(3*sqrt(5)))/8)*(2/5)*(Truncated Edge of Hexakis Icosahedron)*(sqrt(15*(5-sqrt(5))))
Midsphere Radius of Hexakis Icosahedron = ((5+(3*sqrt(5)))/8)*((22*Medium Edge of Hexakis Icosahedron)/(3*(4+sqrt(5))))
Midsphere Radius of Hexakis Icosahedron = Long Edge of Hexakis Icosahedron/8*(5+3*sqrt(5))
Midsphere Radius of Hexakis Icosahedron = 1/8*sqrt(44/15*Total Surface Area of Hexakis Icosahedron/sqrt(10*(417+107*sqrt(5))))*(5+3*sqrt(5))
Midsphere Radius of Hexakis Icosahedron = 1/8*(88/25*Volume of Hexakis Icosahedron/sqrt(6*(185+82*sqrt(5))))^(1/3)*(5+3*sqrt(5))
Midsphere Radius of Hexakis Icosahedron = 1/8*(4*Insphere Radius of Hexakis Icosahedron/sqrt(15/241*(275+119*sqrt(5))))*(5+3*sqrt(5))
Midsphere Radius of Hexakis Icosahedron = 1/8*(6/5*sqrt(10*(417+107*sqrt(5)))/(Surface to Volume Ratio of Hexakis Icosahedron*sqrt(6*(185+82*sqrt(5)))))*(5+3*sqrt(5))

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