Short Edge Of Pentagonal Hexecontahedron Given Surface To Volume Ratio Calculator

Formula Used:

\[ le(Short) = \frac{6 \times (2+3 \times 0.4715756) \times \sqrt{1-0.4715756^2}/(1-2 \times 0.4715756^2)}{AV \times \frac{(1+0.4715756) \times (2+3 \times 0.4715756)}{(1-2 \times 0.4715756^2) \times \sqrt{1-2 \times 0.4715756}}} \]

Short Edge of Pentagonal Hexecontahedron:

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1. What is Short Edge of Pentagonal Hexecontahedron?

The Short Edge of Pentagonal Hexecontahedron is the length of the shortest edge which is the base and middle edge of the axial-symmetric pentagonal faces of the Pentagonal Hexecontahedron. It is a key geometric parameter in this complex polyhedron structure.

2. How Does the Calculator Work?

The calculator uses the formula:

Where:

\( le(Short) \) — Short Edge of Pentagonal Hexecontahedron (m)
\( AV \) — SA:V of Pentagonal Hexecontahedron (1/m)
0.4715756 — Constant value used in the calculation

Explanation: The formula calculates the short edge length based on the surface area to volume ratio of the pentagonal hexecontahedron, using a specific mathematical relationship derived from its geometric properties.

3. Importance of Short Edge Calculation

Details: Calculating the short edge is important for understanding the geometric properties of pentagonal hexecontahedrons, which are used in various mathematical and engineering applications, particularly in the study of complex polyhedral structures and their surface area to volume relationships.

4. Using the Calculator

Tips: Enter the surface area to volume ratio (SA:V) in 1/m. The value must be positive and valid for accurate calculation of the short edge length.

5. Frequently Asked Questions (FAQ)

Q1: What is a Pentagonal Hexecontahedron?
A: A pentagonal hexecontahedron is a polyhedron with 60 pentagonal faces. It is a complex geometric shape studied in mathematics and materials science.

Q2: What does SA:V ratio represent?
A: The surface area to volume ratio indicates how much surface area a shape has relative to its volume, which is important in various physical and chemical processes.

Q3: Why is the constant 0.4715756 used?
A: This constant is derived from the specific geometric properties and mathematical relationships of the pentagonal hexecontahedron structure.

Q4: What units should I use?
A: Use consistent units - SA:V in 1/meter will give the short edge length in meters. You can use any consistent unit system.

Q5: Where is this calculation applied?
A: This type of calculation is used in mathematical research, materials science, crystallography, and the study of complex geometric structures.