Surface to Volume Ratio of Pentagonal Icositetrahedron given Total Surface Area Calculator

Formula Used:

\[ SA:V = \frac{3\sqrt{\frac{22(5[Tribonacci_C]-1)}{(4[Tribonacci_C])-3}}}{\left(\sqrt{\frac{TSA}{3}} \times \left(\frac{(4[Tribonacci_C])-3}{22((5[Tribonacci_C])-1)}\right)^{\frac{1}{4}} \times \sqrt{\frac{11([Tribonacci_C]-4)}{2((20[Tribonacci_C])-37)}}\right)} \]

Surface to Volume Ratio (SA:V):

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1. What is Surface to Volume Ratio of Pentagonal Icositetrahedron?

The surface to volume ratio (SA:V) of a Pentagonal Icositetrahedron is a geometric property that represents the relationship between the total surface area and the volume of this complex polyhedron. It's an important parameter in materials science and geometry.

2. How Does the Calculator Work?

The calculator uses the specialized formula:

Where:

\( TSA \) — Total Surface Area (m²)
\( [Tribonacci_C] \) — Tribonacci constant (≈1.839286755214161)

3. Importance of Surface to Volume Ratio

Details: The SA:V ratio is crucial in various scientific fields including materials science, chemistry, and physics. It affects properties like reactivity, heat transfer, and mechanical strength of materials.

4. Using the Calculator

Tips: Enter the total surface area in square meters. The value must be positive and greater than zero for accurate calculation.

5. Frequently Asked Questions (FAQ)

Q1: What is a Pentagonal Icositetrahedron?
A: A Pentagonal Icositetrahedron is a complex polyhedron with 24 pentagonal faces, making it a Catalan solid.

Q2: What is the Tribonacci constant?
A: The Tribonacci constant is the ratio toward which adjacent Tribonacci numbers tend, approximately equal to 1.839286755214161.

Q3: Why is SA:V ratio important?
A: Higher SA:V ratios indicate more surface area relative to volume, which can enhance properties like catalytic activity and heat dissipation.

Q4: What units are used in this calculation?
A: The calculator uses square meters for surface area and returns the ratio in reciprocal meters (m⁻¹).

Q5: Can this calculator handle very large or small values?
A: The calculator can handle a wide range of values, but extremely large or small numbers may be limited by floating-point precision.