Short Edge Of Pentagonal Hexecontahedron Given Total Surface Area Calculator

Formula Used:

\[ \text{Short Edge} = \sqrt{\frac{\text{Total Surface Area} \times (1 - 2 \times 0.4715756^2)}{30 \times (2 + 3 \times 0.4715756) \times \sqrt{1 - 0.4715756^2}}} \]

Short Edge of Pentagonal Hexecontahedron:

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1. What is the 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 following formula:

\[ \text{Short Edge} = \sqrt{\frac{\text{Total Surface Area} \times (1 - 2 \times 0.4715756^2)}{30 \times (2 + 3 \times 0.4715756) \times \sqrt{1 - 0.4715756^2}}} \]

Where:

Total Surface Area (TSA) — The total surface area of the Pentagonal Hexecontahedron in square meters
0.4715756 — A constant value specific to the geometry of Pentagonal Hexecontahedron

Explanation: This formula derives the short edge length from the total surface area using geometric relationships specific to the Pentagonal Hexecontahedron structure.

3. Importance of Short Edge Calculation

Details: Calculating the short edge is essential for understanding the geometric properties, structural integrity, and spatial characteristics of Pentagonal Hexecontahedron in mathematical modeling and engineering applications.

4. Using the Calculator

Tips: Enter the total surface area in square meters. The value must be positive and valid. The calculator will compute the corresponding short edge length.

5. Frequently Asked Questions (FAQ)

Q1: What is a Pentagonal Hexecontahedron?
A: A Pentagonal Hexecontahedron is a complex polyhedron with 60 pentagonal faces, making it one of the Catalan solids.

Q2: Why is the constant 0.4715756 used in the formula?
A: This constant represents specific geometric relationships and ratios inherent to the Pentagonal Hexecontahedron structure.

Q3: What are typical values for the short edge?
A: The short edge length varies depending on the total surface area, but typically ranges from fractions of a meter to several meters in practical applications.

Q4: Can this formula be used for other polyhedra?
A: No, this formula is specific to the Pentagonal Hexecontahedron due to its unique geometric properties.

Q5: What precision should I expect from the calculation?
A: The calculator provides results with 6 decimal places precision, suitable for most mathematical and engineering applications.