Edge Length of Snub Dodecahedron given Surface to Volume Ratio Calculator

✖Surface to Volume Ratio of Snub Dodecahedron is the numerical ratio of the total surface area of a Snub Dodecahedron to the volume of the Snub Dodecahedron.ⓘ Surface to Volume Ratio of Snub Dodecahedron [R_A/V]

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✖Edge Length of Snub Dodecahedron is the length of any edge of the Snub Dodecahedron.ⓘ Edge Length of Snub Dodecahedron given Surface to Volume Ratio [l_e]

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Edge Length of Snub Dodecahedron given Surface to Volume Ratio Solution

STEP 0: Pre-Calculation Summary

Formula Used

Edge Length of Snub Dodecahedron = (((20*sqrt(3))+(3*sqrt(25+(10*sqrt(5)))))*6*(3-(([phi]/2+sqrt([phi]-5/27)/2)^(1/3)+([phi]/2-sqrt([phi]-5/27)/2)^(1/3))^2)^(3/2))/(Surface to Volume Ratio of Snub Dodecahedron*(((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)))
l_e = (((20*sqrt(3))+(3*sqrt(25+(10*sqrt(5)))))*6*(3-(([phi]/2+sqrt([phi]-5/27)/2)^(1/3)+([phi]/2-sqrt([phi]-5/27)/2)^(1/3))^2)^(3/2))/(R_A/V*(((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)))
This formula uses 1 Constants, 1 Functions, 2 Variables

Constants Used

[phi] - Golden ratio Value Taken As 1.61803398874989484820458683436563811

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.
Surface to Volume Ratio of Snub Dodecahedron - (Measured in 1 per Meter) - Surface to Volume Ratio of Snub Dodecahedron is the numerical ratio of the total surface area of a Snub Dodecahedron to the volume of the Snub Dodecahedron.

STEP 1: Convert Input(s) to Base Unit

Surface to Volume Ratio of Snub Dodecahedron: 0.2 1 per Meter --> 0.2 1 per Meter No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

l_e = (((20*sqrt(3))+(3*sqrt(25+(10*sqrt(5)))))*6*(3-(([phi]/2+sqrt([phi]-5/27)/2)^(1/3)+([phi]/2-sqrt([phi]-5/27)/2)^(1/3))^2)^(3/2))/(R_A/V*(((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))) --> (((20*sqrt(3))+(3*sqrt(25+(10*sqrt(5)))))*6*(3-(([phi]/2+sqrt([phi]-5/27)/2)^(1/3)+([phi]/2-sqrt([phi]-5/27)/2)^(1/3))^2)^(3/2))/(0.2*(((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)))

Evaluating ... ...

l_e = 7.3487066250211

STEP 3: Convert Result to Output's Unit

7.3487066250211 Meter --> No Conversion Required

FINAL ANSWER

7.3487066250211 ≈ 7.348707 Meter <-- Edge Length of Snub Dodecahedron

(Calculation completed in 00.008 seconds)

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< 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 Surface to Volume Ratio Formula

LaTeX Go

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 Surface to Volume Ratio?

Edge Length of Snub Dodecahedron given Surface to Volume Ratio calculator uses Edge Length of Snub Dodecahedron = (((20*sqrt(3))+(3*sqrt(25+(10*sqrt(5)))))*6*(3-(([phi]/2+sqrt([phi]-5/27)/2)^(1/3)+([phi]/2-sqrt([phi]-5/27)/2)^(1/3))^2)^(3/2))/(Surface to Volume Ratio of Snub Dodecahedron*(((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))) to calculate the Edge Length of Snub Dodecahedron, Edge Length of Snub Dodecahedron given Surface to Volume Ratio formula is defined as the length of any edge of the Snub Dodecahedron, and calculated using the surface to volume of the Snub Dodecahedron. Edge Length of Snub Dodecahedron is denoted by l_e symbol.

How to calculate Edge Length of Snub Dodecahedron given Surface to Volume Ratio using this online calculator? To use this online calculator for Edge Length of Snub Dodecahedron given Surface to Volume Ratio, enter Surface to Volume Ratio of Snub Dodecahedron (R_A/V) and hit the calculate button. Here is how the Edge Length of Snub Dodecahedron given Surface to Volume Ratio calculation can be explained with given input values -> 7.348707 = (((20*sqrt(3))+(3*sqrt(25+(10*sqrt(5)))))*6*(3-(([phi]/2+sqrt([phi]-5/27)/2)^(1/3)+([phi]/2-sqrt([phi]-5/27)/2)^(1/3))^2)^(3/2))/(0.2*(((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))).

FAQ

What is Edge Length of Snub Dodecahedron given Surface to Volume Ratio?

Edge Length of Snub Dodecahedron given Surface to Volume Ratio formula is defined as the length of any edge of the Snub Dodecahedron, and calculated using the surface to volume of the Snub Dodecahedron and is represented as l_e = (((20*sqrt(3))+(3*sqrt(25+(10*sqrt(5)))))*6*(3-(([phi]/2+sqrt([phi]-5/27)/2)^(1/3)+([phi]/2-sqrt([phi]-5/27)/2)^(1/3))^2)^(3/2))/(R_A/V*(((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))) or Edge Length of Snub Dodecahedron = (((20*sqrt(3))+(3*sqrt(25+(10*sqrt(5)))))*6*(3-(([phi]/2+sqrt([phi]-5/27)/2)^(1/3)+([phi]/2-sqrt([phi]-5/27)/2)^(1/3))^2)^(3/2))/(Surface to Volume Ratio of Snub Dodecahedron*(((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))). Surface to Volume Ratio of Snub Dodecahedron is the numerical ratio of the total surface area of a Snub Dodecahedron to the volume of the Snub Dodecahedron.

How to calculate Edge Length of Snub Dodecahedron given Surface to Volume Ratio?

Edge Length of Snub Dodecahedron given Surface to Volume Ratio formula is defined as the length of any edge of the Snub Dodecahedron, and calculated using the surface to volume of the Snub Dodecahedron is calculated using Edge Length of Snub Dodecahedron = (((20*sqrt(3))+(3*sqrt(25+(10*sqrt(5)))))*6*(3-(([phi]/2+sqrt([phi]-5/27)/2)^(1/3)+([phi]/2-sqrt([phi]-5/27)/2)^(1/3))^2)^(3/2))/(Surface to Volume Ratio of Snub Dodecahedron*(((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))). To calculate Edge Length of Snub Dodecahedron given Surface to Volume Ratio, you need Surface to Volume Ratio of Snub Dodecahedron (R_A/V). With our tool, you need to enter the respective value for Surface to Volume Ratio 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 Surface to Volume Ratio 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))

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