Edge Length of Truncated Rhombohedron given Circumsphere Radius Calculator

✖Circumsphere Radius of Truncated Rhombohedron is the radius of the sphere that contains the Truncated Rhombohedron in such a way that all the vertices are lying on the sphere.ⓘ Circumsphere Radius of Truncated Rhombohedron [r_c]

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✖Edge Length of Truncated Rhombohedron is the length of the edge that joins the triangular edge with rhombohedral edges on each face of the Truncated Rhombohedron.ⓘ Edge Length of Truncated Rhombohedron given Circumsphere Radius [l_e]

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Edge Length of Truncated Rhombohedron given Circumsphere Radius Solution

STEP 0: Pre-Calculation Summary

Formula Used

Edge Length of Truncated Rhombohedron = ((3-sqrt(5))/2)*((4*Circumsphere Radius of Truncated Rhombohedron)/(sqrt(14-(2*sqrt(5)))))
l_e = ((3-sqrt(5))/2)*((4*r_c)/(sqrt(14-(2*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

Edge Length of Truncated Rhombohedron - (Measured in Meter) - Edge Length of Truncated Rhombohedron is the length of the edge that joins the triangular edge with rhombohedral edges on each face of the Truncated Rhombohedron.
Circumsphere Radius of Truncated Rhombohedron - (Measured in Meter) - Circumsphere Radius of Truncated Rhombohedron is the radius of the sphere that contains the Truncated Rhombohedron in such a way that all the vertices are lying on the sphere.

STEP 1: Convert Input(s) to Base Unit

Circumsphere Radius of Truncated Rhombohedron: 20 Meter --> 20 Meter No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

l_e = ((3-sqrt(5))/2)*((4*r_c)/(sqrt(14-(2*sqrt(5))))) --> ((3-sqrt(5))/2)*((4*20)/(sqrt(14-(2*sqrt(5)))))

Evaluating ... ...

l_e = 9.8995836735288

STEP 3: Convert Result to Output's Unit

9.8995836735288 Meter --> No Conversion Required

FINAL ANSWER

9.8995836735288 ≈ 9.899584 Meter <-- Edge Length of Truncated Rhombohedron

(Calculation completed in 00.004 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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< Edge Length of Truncated Rhombohedron Calculators

Edge Length of Truncated Rhombohedron given Total Surface Area

LaTeX Go Edge Length of Truncated Rhombohedron = ((3-sqrt(5))/2)*(sqrt((2*Total Surface Area of Truncated Rhombohedron)/((3*(sqrt(5+(2*sqrt(5)))))+(5*sqrt(3))-(2*sqrt(15)))))

Edge Length of Truncated Rhombohedron given Circumsphere Radius

LaTeX Go Edge Length of Truncated Rhombohedron = ((3-sqrt(5))/2)*((4*Circumsphere Radius of Truncated Rhombohedron)/(sqrt(14-(2*sqrt(5)))))

Edge Length of Truncated Rhombohedron given Triangular Edge Length

LaTeX Go Edge Length of Truncated Rhombohedron = ((3-sqrt(5))/2)*(Triangular Edge Length of Truncated Rhombohedron/(sqrt(5-(2*sqrt(5)))))

Edge Length of Truncated Rhombohedron given Rhombohedral Edge Length

LaTeX Go Edge Length of Truncated Rhombohedron = (Rhombohedral Edge Length of Truncated Rhombohedron*(3-sqrt(5)))/2

Edge Length of Truncated Rhombohedron given Circumsphere Radius Formula

LaTeX Go

Edge Length of Truncated Rhombohedron = ((3-sqrt(5))/2)*((4*Circumsphere Radius of Truncated Rhombohedron)/(sqrt(14-(2*sqrt(5)))))
l_e = ((3-sqrt(5))/2)*((4*r_c)/(sqrt(14-(2*sqrt(5)))))

What is Truncated Rhombohedron?

The Truncated Rhombohedron is a convex, octahedral polyhedron. It is made up of six equal, irregular, but axially symmetrical pentagons and two equilateral triangles. It has twelve corners; three faces meet at each corner (a triangle and two pentagons or three pentagons). All corner points lie on the same sphere. Opposite faces are parallel. In the stitch, the body stands on a triangular surface, the pentagons virtually form the surface. The number of edges is eighteen.

How to Calculate Edge Length of Truncated Rhombohedron given Circumsphere Radius?

Edge Length of Truncated Rhombohedron given Circumsphere Radius calculator uses Edge Length of Truncated Rhombohedron = ((3-sqrt(5))/2)*((4*Circumsphere Radius of Truncated Rhombohedron)/(sqrt(14-(2*sqrt(5))))) to calculate the Edge Length of Truncated Rhombohedron, Edge Length of Truncated Rhombohedron given Circumsphere Radius formula is defined as the length of the edge that joins the triangular edge with rhombohedral edges on each face of the Truncated Rhombohedron, calculated using its circumsphere radius. Edge Length of Truncated Rhombohedron is denoted by l_e symbol.

How to calculate Edge Length of Truncated Rhombohedron given Circumsphere Radius using this online calculator? To use this online calculator for Edge Length of Truncated Rhombohedron given Circumsphere Radius, enter Circumsphere Radius of Truncated Rhombohedron (r_c) and hit the calculate button. Here is how the Edge Length of Truncated Rhombohedron given Circumsphere Radius calculation can be explained with given input values -> 9.899584 = ((3-sqrt(5))/2)*((4*20)/(sqrt(14-(2*sqrt(5))))).

FAQ

What is Edge Length of Truncated Rhombohedron given Circumsphere Radius?

Edge Length of Truncated Rhombohedron given Circumsphere Radius formula is defined as the length of the edge that joins the triangular edge with rhombohedral edges on each face of the Truncated Rhombohedron, calculated using its circumsphere radius and is represented as l_e = ((3-sqrt(5))/2)*((4*r_c)/(sqrt(14-(2*sqrt(5))))) or Edge Length of Truncated Rhombohedron = ((3-sqrt(5))/2)*((4*Circumsphere Radius of Truncated Rhombohedron)/(sqrt(14-(2*sqrt(5))))). Circumsphere Radius of Truncated Rhombohedron is the radius of the sphere that contains the Truncated Rhombohedron in such a way that all the vertices are lying on the sphere.

How to calculate Edge Length of Truncated Rhombohedron given Circumsphere Radius?

Edge Length of Truncated Rhombohedron given Circumsphere Radius formula is defined as the length of the edge that joins the triangular edge with rhombohedral edges on each face of the Truncated Rhombohedron, calculated using its circumsphere radius is calculated using Edge Length of Truncated Rhombohedron = ((3-sqrt(5))/2)*((4*Circumsphere Radius of Truncated Rhombohedron)/(sqrt(14-(2*sqrt(5))))). To calculate Edge Length of Truncated Rhombohedron given Circumsphere Radius, you need Circumsphere Radius of Truncated Rhombohedron (r_c). With our tool, you need to enter the respective value for Circumsphere Radius of Truncated Rhombohedron 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 Truncated Rhombohedron?

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

Edge Length of Truncated Rhombohedron = (Rhombohedral Edge Length of Truncated Rhombohedron*(3-sqrt(5)))/2
Edge Length of Truncated Rhombohedron = ((3-sqrt(5))/2)*(Triangular Edge Length of Truncated Rhombohedron/(sqrt(5-(2*sqrt(5)))))
Edge Length of Truncated Rhombohedron = ((3-sqrt(5))/2)*(sqrt((2*Total Surface Area of Truncated Rhombohedron)/((3*(sqrt(5+(2*sqrt(5)))))+(5*sqrt(3))-(2*sqrt(15)))))

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