Mid Ridge Length of Great Icosahedron given Long Ridge Length Calculator

Formula Used:

\[ l_{Mid} = \frac{1+\sqrt{5}}{2} \times \frac{10 \times l_{Long}}{\sqrt{2} \times (5+3\sqrt{5})} \]

Mid Ridge Length of Great Icosahedron:

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1. What is Mid Ridge Length of Great Icosahedron?

The Mid Ridge Length of Great Icosahedron is the length of any of the edges that starts from the peak vertex and end on the interior of the pentagon on which each peak of Great Icosahedron is attached.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ l_{Mid} = \frac{1+\sqrt{5}}{2} \times \frac{10 \times l_{Long}}{\sqrt{2} \times (5+3\sqrt{5})} \]

Where:

\( l_{Mid} \) — Mid Ridge Length of Great Icosahedron (m)
\( l_{Long} \) — Long Ridge Length of Great Icosahedron (m)

Explanation: This formula calculates the mid ridge length based on the given long ridge length using the golden ratio and geometric relationships in the great icosahedron.

3. Importance of Mid Ridge Length Calculation

Details: Calculating mid ridge length is important for understanding the geometric properties and proportions of the great icosahedron, which has applications in mathematics, architecture, and structural design.

4. Using the Calculator

Tips: Enter the long ridge length in meters. The value must be positive and greater than zero.

5. Frequently Asked Questions (FAQ)

Q1: What is a great icosahedron?
A: The great icosahedron is one of the four Kepler-Poinsot polyhedra, consisting of 20 triangular faces that intersect each other.

Q2: How is the mid ridge length different from other edges?
A: The mid ridge length specifically refers to edges that connect peak vertices to the interior of pentagonal faces in the great icosahedron structure.

Q3: What are the applications of this calculation?
A: This calculation is useful in geometric modeling, architectural design, and understanding the mathematical properties of complex polyhedra.

Q4: How accurate is this formula?
A: The formula is mathematically exact and provides precise calculations based on the geometric relationships within the great icosahedron.

Q5: Can this calculator handle different units?
A: The calculator uses meters as the default unit, but you can convert other units to meters before inputting the value.