Nonsymmetry Diagonal Of Deltoidal Hexecontahedron Given Total Surface Area Calculator

Formula Used:

\[ d_{NonSymmetry} = \frac{\sqrt{\frac{470 + 156\sqrt{5}}{5}}}{11} \times \sqrt{\frac{11 \times TSA}{9 \times \sqrt{10(157 + 31\sqrt{5})}}} \]

NonSymmetry Diagonal:

Unit Converter ▲

Unit Converter ▼

From:	To:

1. What is NonSymmetry Diagonal of Deltoidal Hexecontahedron?

The NonSymmetry Diagonal of Deltoidal Hexecontahedron is the length of the diagonal which divides the deltoid faces of Deltoidal Hexecontahedron into two isosceles triangles. It is an important geometric property of this polyhedron.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ d_{NonSymmetry} = \frac{\sqrt{\frac{470 + 156\sqrt{5}}{5}}}{11} \times \sqrt{\frac{11 \times TSA}{9 \times \sqrt{10(157 + 31\sqrt{5})}}} \]

Where:

\( d_{NonSymmetry} \) — NonSymmetry Diagonal (m)
\( TSA \) — Total Surface Area (m²)
\( \sqrt{5} \) — Square root of 5 (approximately 2.23607)

Explanation: This formula calculates the NonSymmetry Diagonal based on the total surface area of the Deltoidal Hexecontahedron, incorporating mathematical constants related to its geometric properties.

3. Importance of NonSymmetry Diagonal Calculation

Details: Calculating the NonSymmetry Diagonal is essential for understanding the geometric properties and spatial relationships within the Deltoidal Hexecontahedron, which has applications in crystallography, architecture, and mathematical research.

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 Deltoidal Hexecontahedron?
A: A Deltoidal Hexecontahedron is a Catalan solid with 60 deltoid faces, 120 edges, and 62 vertices.

Q2: Why is this diagonal called "NonSymmetry"?
A: It's called NonSymmetry Diagonal because it divides the deltoid faces asymmetrically into two isosceles triangles.

Q3: What are typical values for the NonSymmetry Diagonal?
A: The value depends on the size of the polyhedron. For a standard Deltoidal Hexecontahedron, it's proportional to the cube root of the volume.

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

Q5: How accurate is this calculation?
A: The calculation is mathematically exact when using the precise formula, though computational rounding may introduce minor errors in decimal representation.