Edge Length of Icosidodecahedron given Pentagonal Face Height Calculator

✖Pentagonal Face Height of Icosidodecahedron is the shortest distance between an edge and the vertically opposite corner, of any of the pentagonal faces of the Icosidodecahedron.ⓘ Pentagonal Face Height of Icosidodecahedron [h_Pentagon]

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✖Edge Length of Icosidodecahedron is the length of any edge of the Icosidodecahedron.ⓘ Edge Length of Icosidodecahedron given Pentagonal Face Height [l_e]

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Edge Length of Icosidodecahedron given Pentagonal Face Height Solution

STEP 0: Pre-Calculation Summary

Formula Used

Edge Length of Icosidodecahedron = (2*Pentagonal Face Height of Icosidodecahedron)/sqrt(5+(2*sqrt(5)))
l_e = (2*h_Pentagon)/sqrt(5+(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 Icosidodecahedron - (Measured in Meter) - Edge Length of Icosidodecahedron is the length of any edge of the Icosidodecahedron.
Pentagonal Face Height of Icosidodecahedron - (Measured in Meter) - Pentagonal Face Height of Icosidodecahedron is the shortest distance between an edge and the vertically opposite corner, of any of the pentagonal faces of the Icosidodecahedron.

STEP 1: Convert Input(s) to Base Unit

Pentagonal Face Height of Icosidodecahedron: 15 Meter --> 15 Meter No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

l_e = (2*h_Pentagon)/sqrt(5+(2*sqrt(5))) --> (2*15)/sqrt(5+(2*sqrt(5)))

Evaluating ... ...

l_e = 9.74759088698719

STEP 3: Convert Result to Output's Unit

9.74759088698719 Meter --> No Conversion Required

FINAL ANSWER

9.74759088698719 ≈ 9.747591 Meter <-- Edge Length of Icosidodecahedron

(Calculation completed in 00.004 seconds)

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< Edge Length of Icosidodecahedron Calculators

Edge Length of Icosidodecahedron given Total Surface Area

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

Edge Length of Icosidodecahedron given Midsphere Radius

LaTeX Go Edge Length of Icosidodecahedron = (2*Midsphere Radius of Icosidodecahedron)/(sqrt(5+(2*sqrt(5))))

Edge Length of Icosidodecahedron given Volume

LaTeX Go Edge Length of Icosidodecahedron = ((6*Volume of Icosidodecahedron)/(45+(17*sqrt(5))))^(1/3)

Edge Length of Icosidodecahedron given Circumsphere Radius

LaTeX Go Edge Length of Icosidodecahedron = (2*Circumsphere Radius of Icosidodecahedron)/(1+sqrt(5))

Edge Length of Icosidodecahedron given Pentagonal Face Height Formula

LaTeX Go

Edge Length of Icosidodecahedron = (2*Pentagonal Face Height of Icosidodecahedron)/sqrt(5+(2*sqrt(5)))
l_e = (2*h_Pentagon)/sqrt(5+(2*sqrt(5)))

What is an Icosidodecahedron?

In geometry, an Icosidodecahedron is a closed and convex polyhedron with 20 (icosi) triangular faces and 12 (dodeca) pentagonal faces. An Icosidodecahedron has 30 identical vertices, with 2 triangles and 2 pentagons meeting at each. And 60 identical edges, each separating a triangle from a pentagon. As such it is one of the Archimedean solids and more particularly, a quasiregular polyhedron.

How to Calculate Edge Length of Icosidodecahedron given Pentagonal Face Height?

Edge Length of Icosidodecahedron given Pentagonal Face Height calculator uses Edge Length of Icosidodecahedron = (2*Pentagonal Face Height of Icosidodecahedron)/sqrt(5+(2*sqrt(5))) to calculate the Edge Length of Icosidodecahedron, Edge Length of Icosidodecahedron given Pentagonal Face Height formula is defined as the length of any edge of the Icosidodecahedron, and calculated using the pentagonal face height of the Icosidodecahedron. Edge Length of Icosidodecahedron is denoted by l_e symbol.

How to calculate Edge Length of Icosidodecahedron given Pentagonal Face Height using this online calculator? To use this online calculator for Edge Length of Icosidodecahedron given Pentagonal Face Height, enter Pentagonal Face Height of Icosidodecahedron (h_Pentagon) and hit the calculate button. Here is how the Edge Length of Icosidodecahedron given Pentagonal Face Height calculation can be explained with given input values -> 9.747591 = (2*15)/sqrt(5+(2*sqrt(5))).

FAQ

What is Edge Length of Icosidodecahedron given Pentagonal Face Height?

Edge Length of Icosidodecahedron given Pentagonal Face Height formula is defined as the length of any edge of the Icosidodecahedron, and calculated using the pentagonal face height of the Icosidodecahedron and is represented as l_e = (2*h_Pentagon)/sqrt(5+(2*sqrt(5))) or Edge Length of Icosidodecahedron = (2*Pentagonal Face Height of Icosidodecahedron)/sqrt(5+(2*sqrt(5))). Pentagonal Face Height of Icosidodecahedron is the shortest distance between an edge and the vertically opposite corner, of any of the pentagonal faces of the Icosidodecahedron.

How to calculate Edge Length of Icosidodecahedron given Pentagonal Face Height?

Edge Length of Icosidodecahedron given Pentagonal Face Height formula is defined as the length of any edge of the Icosidodecahedron, and calculated using the pentagonal face height of the Icosidodecahedron is calculated using Edge Length of Icosidodecahedron = (2*Pentagonal Face Height of Icosidodecahedron)/sqrt(5+(2*sqrt(5))). To calculate Edge Length of Icosidodecahedron given Pentagonal Face Height, you need Pentagonal Face Height of Icosidodecahedron (h_Pentagon). With our tool, you need to enter the respective value for Pentagonal Face Height of Icosidodecahedron 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 Icosidodecahedron?

In this formula, Edge Length of Icosidodecahedron uses Pentagonal Face Height of Icosidodecahedron. We can use 3 other way(s) to calculate the same, which is/are as follows -

Edge Length of Icosidodecahedron = sqrt(Total Surface Area of Icosidodecahedron/((5*sqrt(3))+(3*sqrt(25+(10*sqrt(5))))))
Edge Length of Icosidodecahedron = ((6*Volume of Icosidodecahedron)/(45+(17*sqrt(5))))^(1/3)
Edge Length of Icosidodecahedron = (2*Circumsphere Radius of Icosidodecahedron)/(1+sqrt(5))

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