Volume of Pentagonal Icositetrahedron Calculator

Volume of Pentagonal Icositetrahedron Formula:

\[ V = l_{e(Snub\ Cube)}^3 \times \sqrt{\frac{11 \times ([Tribonacci_C] - 4)}{2 \times ((20 \times [Tribonacci_C]) - 37)}} \]

Volume of Pentagonal Icositetrahedron:

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1. What is the Volume of Pentagonal Icositetrahedron?

The Volume of Pentagonal Icositetrahedron is the quantity of three dimensional space enclosed by the entire surface of Pentagonal Icositetrahedron. It is a Catalan solid that is dual to the snub cube.

2. How Does the Calculator Work?

The calculator uses the following formula:

\[ V = l_{e(Snub\ Cube)}^3 \times \sqrt{\frac{11 \times ([Tribonacci_C] - 4)}{2 \times ((20 \times [Tribonacci_C]) - 37)}} \]

Where:

\( V \) — Volume of Pentagonal Icositetrahedron (m³)
\( l_{e(Snub\ Cube)} \) — Snub Cube Edge of Pentagonal Icositetrahedron (m)
\( [Tribonacci_C] \) — Tribonacci constant (≈1.839286755214161)

Explanation: The formula calculates the volume based on the edge length of the snub cube and involves the mathematical constant Tribonacci constant.

3. Importance of Volume Calculation

Details: Calculating the volume of geometric solids is fundamental in mathematics, physics, engineering, and various scientific applications. It helps in understanding spatial properties and material requirements.

4. Using the Calculator

Tips: Enter the Snub Cube Edge length in meters. The value must be positive and valid.

5. Frequently Asked Questions (FAQ)

Q1: What is a Pentagonal Icositetrahedron?
A: A Pentagonal Icositetrahedron is a Catalan solid with 24 faces, each of which is an irregular pentagon. It is the dual of the snub cube.

Q2: What is the Tribonacci constant?
A: The Tribonacci constant is the real root of the equation x³ - x² - x - 1 = 0, approximately equal to 1.839286755214161.

Q3: How accurate is this calculation?
A: The calculation is mathematically precise based on the given formula and the defined Tribonacci constant value.

Q4: Can this calculator be used for other polyhedra?
A: No, this calculator is specifically designed for calculating the volume of Pentagonal Icositetrahedron only.

Q5: What units should I use for input?
A: The calculator expects input in meters, and the result will be in cubic meters. You can convert from other units as needed.