Total Surface Area Of Deltoidal Hexecontahedron Given Short Edge Calculator

Formula Used:

\[ TSA = \frac{9}{11} \times \sqrt{10 \times (157 + 31 \times \sqrt{5})} \times \left( \frac{22 \times l_{short}}{3 \times (7 - \sqrt{5})} \right)^2 \]

Total Surface Area of Deltoidal Hexecontahedron:

Unit Converter ▲

Unit Converter ▼

From:	To:

1. What is the Total Surface Area of Deltoidal Hexecontahedron?

The Total Surface Area of Deltoidal Hexecontahedron is the total quantity of plane enclosed on the entire surface of the Deltoidal Hexecontahedron. It is a Catalan solid with 60 congruent deltoid faces.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ TSA = \frac{9}{11} \times \sqrt{10 \times (157 + 31 \times \sqrt{5})} \times \left( \frac{22 \times l_{short}}{3 \times (7 - \sqrt{5})} \right)^2 \]

Where:

\( TSA \) — Total Surface Area of Deltoidal Hexecontahedron (m²)
\( l_{short} \) — Short Edge of Deltoidal Hexecontahedron (m)
\( \sqrt{5} \) — Mathematical constant approximately equal to 2.23607

Explanation: This formula calculates the total surface area based on the length of the short edge of the deltoidal faces, incorporating mathematical constants and geometric relationships specific to this polyhedron.

3. Importance of Surface Area Calculation

Details: Calculating the surface area of geometric solids is fundamental in various fields including architecture, materials science, and 3D modeling. It helps in determining material requirements, heat transfer properties, and structural characteristics.

4. Using the Calculator

Tips: Enter the length of the short edge in meters. The value must be positive and greater than zero. The calculator will compute the total surface area based on the geometric properties of the deltoidal hexecontahedron.

5. Frequently Asked Questions (FAQ)

Q1: What is a Deltoidal Hexecontahedron?
A: A Deltoidal Hexecontahedron is a Catalan solid with 60 congruent deltoid faces, 120 edges, and 62 vertices. It is the dual polyhedron of the rhombicosidodecahedron.

Q2: What are the applications of this calculation?
A: This calculation is useful in geometric modeling, architectural design, material science calculations, and educational purposes for understanding polyhedral properties.

Q3: What units should be used for input?
A: The calculator uses meters as the default unit for length input. Ensure consistent units throughout your calculations.

Q4: How accurate is the calculation?
A: The calculation uses precise mathematical constants and formulas, providing results accurate to six decimal places as displayed.

Q5: Can this calculator handle very small or large values?
A: The calculator can handle a wide range of positive values, though extremely large values may be limited by computational precision.