Edge Length of Snub Dodecahedron given Midsphere Radius Calculator

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

+10%

-10%

✖Edge Length of Snub Dodecahedron is the length of any edge of the Snub Dodecahedron.ⓘ Edge Length of Snub Dodecahedron given Midsphere Radius [l_e]

⎘ Copy

👎

Formula

LaTeX

Reset

👍

Download Snub Dodecahedron Formula PDF PDF Image

Edge Length of Snub Dodecahedron given Midsphere Radius Solution

STEP 0: Pre-Calculation Summary

Formula Used

Edge Length of Snub Dodecahedron = (2*Midsphere Radius of Snub Dodecahedron)/sqrt(1/(1-0.94315125924))
l_e = (2*r_m)/sqrt(1/(1-0.94315125924))
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

Edge Length of Snub Dodecahedron - (Measured in Meter) - Edge Length of Snub Dodecahedron is the length of any edge of the Snub Dodecahedron.
Midsphere Radius of Snub Dodecahedron - (Measured in Meter) - Midsphere Radius of Snub Dodecahedron is the radius of the sphere for which all the edges of the Snub Dodecahedron become a tangent line on that sphere.

STEP 1: Convert Input(s) to Base Unit

Midsphere Radius of Snub Dodecahedron: 21 Meter --> 21 Meter No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

l_e = (2*r_m)/sqrt(1/(1-0.94315125924)) --> (2*21)/sqrt(1/(1-0.94315125924))

Evaluating ... ...

l_e = 10.0140490662189

STEP 3: Convert Result to Output's Unit

10.0140490662189 Meter --> No Conversion Required

FINAL ANSWER

10.0140490662189 ≈ 10.01405 Meter <-- Edge Length of Snub Dodecahedron

(Calculation completed in 00.004 seconds)

You are here -

Home » Math » Geometry » 3D Geometry » Archimedean Solids » Snub Dodecahedron » Edge Length of Snub Dodecahedron » Edge Length of Snub Dodecahedron given Midsphere Radius

Credits

Created by Mona Gladys

St Joseph's College (SJC), Bengaluru

Mona Gladys has created this Calculator and 2000+ more calculators!

Verified by Shweta Patil

Walchand College of Engineering (WCE), Sangli

Shweta Patil has verified this Calculator and 1100+ more calculators!

< Edge Length of Snub Dodecahedron Calculators

Edge Length of Snub Dodecahedron given Volume

LaTeX Go Edge Length of Snub Dodecahedron = ((Volume of Snub Dodecahedron*6*(3-(([phi]/2+sqrt([phi]-5/27)/2)^(1/3)+([phi]/2-sqrt([phi]-5/27)/2)^(1/3))^2)^(3/2))/(((12*((3*[phi])+1))*((([phi]/2+sqrt([phi]-5/27)/2)^(1/3)+([phi]/2-sqrt([phi]-5/27)/2)^(1/3))^2)-(((36*[phi])+7)*(([phi]/2+sqrt([phi]-5/27)/2)^(1/3)+([phi]/2-sqrt([phi]-5/27)/2)^(1/3))))-((53*[phi])+6)))^(1/3)

Edge Length of Snub Dodecahedron given Total Surface Area

LaTeX Go Edge Length of Snub Dodecahedron = sqrt(Total Surface Area of Snub Dodecahedron/((20*sqrt(3))+(3*sqrt(25+(10*sqrt(5))))))

Edge Length of Snub Dodecahedron given Circumsphere Radius

LaTeX Go Edge Length of Snub Dodecahedron = (2*Circumsphere Radius of Snub Dodecahedron)/sqrt((2-0.94315125924)/(1-0.94315125924))

Edge Length of Snub Dodecahedron given Midsphere Radius

LaTeX Go Edge Length of Snub Dodecahedron = (2*Midsphere Radius of Snub Dodecahedron)/sqrt(1/(1-0.94315125924))

Edge Length of Snub Dodecahedron given Midsphere Radius Formula

LaTeX Go

Edge Length of Snub Dodecahedron = (2*Midsphere Radius of Snub Dodecahedron)/sqrt(1/(1-0.94315125924))
l_e = (2*r_m)/sqrt(1/(1-0.94315125924))

What is a Snub Dodecahedron?

In geometry, the Snub Dodecahedron, or snub icosidodecahedron, is an Archimedean solid, one of thirteen convex isogonal non-prismatic solids constructed by two or more types of regular polygon faces. The Snub Dodecahedron has 92 faces (the most of the 13 Archimedean solids): 12 are pentagons and the other 80 are equilateral triangles. It also has 150 edges, and 60 vertices. Each vertex is identical in such a way that, 4 equilateral triangular faces and 1 pentagonal face are joining together at each vertex. It has two distinct forms, which are mirror images (or "enantiomorphs") of each other. The union of both forms is a compound of two Snub Dodecahedra, and the convex hull of both forms is a truncated icosidodecahedron.

How to Calculate Edge Length of Snub Dodecahedron given Midsphere Radius?

Edge Length of Snub Dodecahedron given Midsphere Radius calculator uses Edge Length of Snub Dodecahedron = (2*Midsphere Radius of Snub Dodecahedron)/sqrt(1/(1-0.94315125924)) to calculate the Edge Length of Snub Dodecahedron, Edge Length of Snub Dodecahedron given Midsphere Radius formula is defined as the length of any edge of the Snub Dodecahedron, and calculated using the midsphere radius of the Snub Dodecahedron. Edge Length of Snub Dodecahedron is denoted by l_e symbol.

How to calculate Edge Length of Snub Dodecahedron given Midsphere Radius using this online calculator? To use this online calculator for Edge Length of Snub Dodecahedron given Midsphere Radius, enter Midsphere Radius of Snub Dodecahedron (r_m) and hit the calculate button. Here is how the Edge Length of Snub Dodecahedron given Midsphere Radius calculation can be explained with given input values -> 10.01405 = (2*21)/sqrt(1/(1-0.94315125924)).

FAQ

What is Edge Length of Snub Dodecahedron given Midsphere Radius?

Edge Length of Snub Dodecahedron given Midsphere Radius formula is defined as the length of any edge of the Snub Dodecahedron, and calculated using the midsphere radius of the Snub Dodecahedron and is represented as l_e = (2*r_m)/sqrt(1/(1-0.94315125924)) or Edge Length of Snub Dodecahedron = (2*Midsphere Radius of Snub Dodecahedron)/sqrt(1/(1-0.94315125924)). Midsphere Radius of Snub Dodecahedron is the radius of the sphere for which all the edges of the Snub Dodecahedron become a tangent line on that sphere.

How to calculate Edge Length of Snub Dodecahedron given Midsphere Radius?

Edge Length of Snub Dodecahedron given Midsphere Radius formula is defined as the length of any edge of the Snub Dodecahedron, and calculated using the midsphere radius of the Snub Dodecahedron is calculated using Edge Length of Snub Dodecahedron = (2*Midsphere Radius of Snub Dodecahedron)/sqrt(1/(1-0.94315125924)). To calculate Edge Length of Snub Dodecahedron given Midsphere Radius, you need Midsphere Radius of Snub Dodecahedron (r_m). With our tool, you need to enter the respective value for Midsphere Radius of Snub Dodecahedron 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 Edge Length of Snub Dodecahedron?

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

Edge Length of Snub Dodecahedron = sqrt(Total Surface Area of Snub Dodecahedron/((20*sqrt(3))+(3*sqrt(25+(10*sqrt(5))))))
Edge Length of Snub Dodecahedron = ((Volume of Snub Dodecahedron*6*(3-(([phi]/2+sqrt([phi]-5/27)/2)^(1/3)+([phi]/2-sqrt([phi]-5/27)/2)^(1/3))^2)^(3/2))/(((12*((3*[phi])+1))*((([phi]/2+sqrt([phi]-5/27)/2)^(1/3)+([phi]/2-sqrt([phi]-5/27)/2)^(1/3))^2)-(((36*[phi])+7)*(([phi]/2+sqrt([phi]-5/27)/2)^(1/3)+([phi]/2-sqrt([phi]-5/27)/2)^(1/3))))-((53*[phi])+6)))^(1/3)
Edge Length of Snub Dodecahedron = (2*Circumsphere Radius of Snub Dodecahedron)/sqrt((2-0.94315125924)/(1-0.94315125924))

Home

FREE PDFs

🔍 Search