Insphere Radius of Octahedron Calculator

✖Edge Length of Octahedron is the length of any of edges of the Octahedron or the distance between any pair of adjacent vertices of the Octahedron.ⓘ Edge Length of Octahedron [l_e]

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

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Formula

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Insphere Radius of Octahedron

Formula

`"r"_{"i"} = "l"_{"e"}/sqrt(6)`

Example

`"4.082483m"="10m"/sqrt(6)`

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Insphere Radius of Octahedron Solution

STEP 0: Pre-Calculation Summary

Formula Used

Insphere Radius of Octahedron = Edge Length of Octahedron/sqrt(6)
r_i = l_e/sqrt(6)
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 Octahedron - (Measured in Meter) - Insphere Radius of Octahedron is the radius of the sphere that is contained by the Octahedron in such a way that all the faces are just touching the sphere.
Edge Length of Octahedron - (Measured in Meter) - Edge Length of Octahedron is the length of any of edges of the Octahedron or the distance between any pair of adjacent vertices of the Octahedron.

STEP 1: Convert Input(s) to Base Unit

Edge Length of Octahedron: 10 Meter --> 10 Meter No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

r_i = l_e/sqrt(6) --> 10/sqrt(6)

Evaluating ... ...

r_i = 4.08248290463863

STEP 3: Convert Result to Output's Unit

4.08248290463863 Meter --> No Conversion Required

FINAL ANSWER

4.08248290463863 ≈ 4.082483 Meter <-- Insphere Radius of Octahedron

(Calculation completed in 00.011 seconds)

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< 7 Insphere Radius of Octahedron Calculators

Insphere Radius of Octahedron given Total Surface Area

Go Insphere Radius of Octahedron = sqrt(Total Surface Area of Octahedron/(2*sqrt(3)))/sqrt(6)

Insphere Radius of Octahedron given Volume

Go Insphere Radius of Octahedron = ((3*Volume of Octahedron)/sqrt(2))^(1/3)/sqrt(6)

Insphere Radius of Octahedron given Circumsphere Radius

Go Insphere Radius of Octahedron = Circumsphere Radius of Octahedron/sqrt(3)

Insphere Radius of Octahedron given Midsphere Radius

Go Insphere Radius of Octahedron = sqrt(2/3)*Midsphere Radius of Octahedron

Insphere Radius of Octahedron given Space Diagonal

Go Insphere Radius of Octahedron = Space Diagonal of Octahedron/(2*sqrt(3))

Insphere Radius of Octahedron

Go Insphere Radius of Octahedron = Edge Length of Octahedron/sqrt(6)

Insphere Radius of Octahedron given Surface to Volume Ratio

Go Insphere Radius of Octahedron = 3/Surface to Volume Ratio of Octahedron

< 9 Radius of Octahedron Calculators

Insphere Radius of Octahedron given Total Surface Area

Go Insphere Radius of Octahedron = sqrt(Total Surface Area of Octahedron/(2*sqrt(3)))/sqrt(6)

Circumsphere Radius of Octahedron given Insphere Radius

Go Circumsphere Radius of Octahedron = sqrt(3)*Insphere Radius of Octahedron

Midsphere Radius of Octahedron given Space Diagonal

Go Midsphere Radius of Octahedron = Space Diagonal of Octahedron/(2*sqrt(2))

Insphere Radius of Octahedron given Midsphere Radius

Go Insphere Radius of Octahedron = sqrt(2/3)*Midsphere Radius of Octahedron

Midsphere Radius of Octahedron given Insphere Radius

Go Midsphere Radius of Octahedron = sqrt(3/2)*Insphere Radius of Octahedron

Circumsphere Radius of Octahedron

Go Circumsphere Radius of Octahedron = Edge Length of Octahedron/sqrt(2)

Insphere Radius of Octahedron

Go Insphere Radius of Octahedron = Edge Length of Octahedron/sqrt(6)

Circumsphere Radius of Octahedron given Space Diagonal

Go Circumsphere Radius of Octahedron = Space Diagonal of Octahedron/2

Midsphere Radius of Octahedron

Go Midsphere Radius of Octahedron = Edge Length of Octahedron/2

Insphere Radius of Octahedron Formula

Insphere Radius of Octahedron = Edge Length of Octahedron/sqrt(6)
r_i = l_e/sqrt(6)

What is an Octahedron?

An Octahedron is a symmetric and closed three dimensional shape with 8 identical equilateral triangular faces. It is a Platonic solid, which has 8 faces, 6 vertices and 12 edges. At each vertex, four equilateral triangular faces meet and at each edge, two equilateral triangular faces meet.

What are Platonic Solids?

In three-dimensional space, a Platonic solid is a regular, convex polyhedron. It is constructed by congruent (identical in shape and size), regular (all angles equal and all sides equal), polygonal faces with the same number of faces meeting at each vertex. Five solids who meet this criteria are Tetrahedron {3,3} , Cube {4,3} , Octahedron {3,4} , Dodecahedron {5,3} , Icosahedron {3,5} ; where in {p, q}, p represents the number of edges in a face and q represents the number of edges meeting at a vertex; {p, q} is the Schläfli symbol.

How to Calculate Insphere Radius of Octahedron?

Insphere Radius of Octahedron calculator uses Insphere Radius of Octahedron = Edge Length of Octahedron/sqrt(6) to calculate the Insphere Radius of Octahedron, Insphere Radius of Octahedron formula is defined as the radius of the sphere that is contained by the Octahedron in such a way that all the faces just touching the sphere. Insphere Radius of Octahedron is denoted by r_i symbol.

How to calculate Insphere Radius of Octahedron using this online calculator? To use this online calculator for Insphere Radius of Octahedron, enter Edge Length of Octahedron (l_e) and hit the calculate button. Here is how the Insphere Radius of Octahedron calculation can be explained with given input values -> 4.082483 = 10/sqrt(6).

FAQ

What is Insphere Radius of Octahedron?

Insphere Radius of Octahedron formula is defined as the radius of the sphere that is contained by the Octahedron in such a way that all the faces just touching the sphere and is represented as r_i = l_e/sqrt(6) or Insphere Radius of Octahedron = Edge Length of Octahedron/sqrt(6). Edge Length of Octahedron is the length of any of edges of the Octahedron or the distance between any pair of adjacent vertices of the Octahedron.

How to calculate Insphere Radius of Octahedron?

Insphere Radius of Octahedron formula is defined as the radius of the sphere that is contained by the Octahedron in such a way that all the faces just touching the sphere is calculated using Insphere Radius of Octahedron = Edge Length of Octahedron/sqrt(6). To calculate Insphere Radius of Octahedron, you need Edge Length of Octahedron (l_e). With our tool, you need to enter the respective value for Edge Length of Octahedron 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 Octahedron?

In this formula, Insphere Radius of Octahedron uses Edge Length of Octahedron. We can use 8 other way(s) to calculate the same, which is/are as follows -

Insphere Radius of Octahedron = sqrt(2/3)*Midsphere Radius of Octahedron
Insphere Radius of Octahedron = Space Diagonal of Octahedron/(2*sqrt(3))
Insphere Radius of Octahedron = Circumsphere Radius of Octahedron/sqrt(3)
Insphere Radius of Octahedron = sqrt(Total Surface Area of Octahedron/(2*sqrt(3)))/sqrt(6)
Insphere Radius of Octahedron = 3/Surface to Volume Ratio of Octahedron
Insphere Radius of Octahedron = ((3*Volume of Octahedron)/sqrt(2))^(1/3)/sqrt(6)
Insphere Radius of Octahedron = sqrt(2/3)*Midsphere Radius of Octahedron
Insphere Radius of Octahedron = sqrt(Total Surface Area of Octahedron/(2*sqrt(3)))/sqrt(6)

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