Long Edge Of Deltoidal Hexecontahedron Given Volume Calculator

Formula Used:

\[ Long Edge = \left( \frac{11 \times Volume}{45 \times \sqrt{\frac{370 + 164\sqrt{5}}{25}}} \right)^{1/3} \]

Long Edge of Deltoidal Hexecontahedron:

Unit Converter ▲

Unit Converter ▼

From:	To:

1. What is Long Edge of Deltoidal Hexecontahedron?

The Long Edge of Deltoidal Hexecontahedron is the length of the longest edge of the identical deltoidal faces that make up this complex polyhedron. It is a key dimensional parameter in understanding the geometry and properties of this shape.

2. How Does the Calculator Work?

The calculator uses the mathematical formula:

\[ Long Edge = \left( \frac{11 \times Volume}{45 \times \sqrt{\frac{370 + 164\sqrt{5}}{25}}} \right)^{1/3} \]

Where:

\( Volume \) — Volume of the Deltoidal Hexecontahedron (m³)
\( \sqrt{} \) — Square root function
\( \sqrt{5} \) — Mathematical constant approximately equal to 2.23607

Explanation: This formula derives from the geometric relationships within the deltoidal hexecontahedron, connecting the volume to the long edge length through precise mathematical constants.

3. Importance of Long Edge Calculation

Details: Calculating the long edge is essential for understanding the proportions and scaling of deltoidal hexecontahedrons in various applications, including crystallography, architectural design, and mathematical modeling.

4. Using the Calculator

Tips: Enter the volume of the deltoidal hexecontahedron in cubic meters. The volume must be a positive value greater than zero for accurate calculation.

5. Frequently Asked Questions (FAQ)

Q1: What is a Deltoidal Hexecontahedron?
A: A deltoidal hexecontahedron is a polyhedron with 60 deltoidal (kite-shaped) faces. It is one of the Catalan solids, dual to the rhombicosidodecahedron.

Q2: What are typical volume values for this shape?
A: Volume values depend on the scale of the polyhedron. For standard unit shapes, volumes typically range from fractions to several cubic units.

Q3: How accurate is this calculation?
A: The calculation is mathematically precise, using exact constants and formulas derived from geometric principles.

Q4: Can this formula be used for other polyhedrons?
A: No, this specific formula applies only to the deltoidal hexecontahedron. Other polyhedrons have different geometric relationships.

Q5: What practical applications does this calculation have?
A: This calculation is useful in fields like materials science, architecture, and 3D modeling where precise geometric measurements are required.