Short Edge Of Deltoidal Hexecontahedron Given Volume Calculator

Formula Used:

\[ Short Edge = \frac{3}{22} \times (7 - \sqrt{5}) \times \left( \frac{11 \times V}{45 \times \sqrt{\frac{370 + 164 \times \sqrt{5}}{25}}} \right)^{\frac{1}{3}} \]

Short Edge of Deltoidal Hexecontahedron:

Unit Converter ▲

Unit Converter ▼

From:	To:

1. What is the Short Edge of Deltoidal Hexecontahedron?

The short edge of a deltoidal hexecontahedron is the length of the shortest edge of the identical deltoidal faces that make up this polyhedron. It is one of the key dimensional parameters that define the geometry of this complex shape.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ Short Edge = \frac{3}{22} \times (7 - \sqrt{5}) \times \left( \frac{11 \times V}{45 \times \sqrt{\frac{370 + 164 \times \sqrt{5}}{25}}} \right)^{\frac{1}{3}} \]

Where:

\( V \) — Volume of Deltoidal Hexecontahedron (m³)
\( \sqrt{5} \) — Square root of 5 (approximately 2.23607)

Explanation: This formula calculates the short edge length based on the given volume of the deltoidal hexecontahedron, incorporating mathematical constants and geometric relationships specific to this polyhedron.

3. Importance of Short Edge Calculation

Details: Calculating the short edge from volume is important for geometric analysis, 3D modeling, and understanding the proportional relationships within deltoidal hexecontahedrons. It helps in reconstructing the complete geometry when only the volume is known.

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 Catalan solid with 60 deltoidal (kite-shaped) faces, 120 edges, and 62 vertices.

Q2: Why is the formula so complex?
A: The complexity arises from the intricate geometric relationships and mathematical constants involved in describing this polyhedron's properties.

Q3: What are typical volume values for this shape?
A: Volume values depend on the specific dimensions, but typically range from small fractions to larger values depending on the scale of the polyhedron.

Q4: Can this calculator handle very large volumes?
A: Yes, the calculator can handle large volume values, though extremely large values may be limited by PHP's floating point precision.

Q5: Is this calculation reversible?
A: Yes, there are corresponding formulas to calculate volume from edge lengths, maintaining the mathematical relationship between these parameters.