Total Surface Area of Rhombic Triacontahedron Calculator

Total Surface Area of Rhombic Triacontahedron Formula:

\[ TSA = 12 \times le^2 \times \sqrt{5} \]

Total Surface Area (TSA):

Unit Converter ▲

Unit Converter ▼

From:	To:

1. What is the Total Surface Area of Rhombic Triacontahedron?

The Total Surface Area of a Rhombic Triacontahedron refers to the total quantity of plane enclosed on the entire surface of this polyhedron. A Rhombic Triacontahedron is a convex polyhedron with 30 rhombic faces, 32 vertices, and 60 edges.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ TSA = 12 \times le^2 \times \sqrt{5} \]

Where:

\( TSA \) — Total Surface Area of Rhombic Triacontahedron (m²)
\( le \) — Edge Length of Rhombic Triacontahedron (m)
\( \sqrt{5} \) — Square root of 5 (approximately 2.23607)

Explanation: The formula calculates the total surface area by multiplying 12 times the square of the edge length times the square root of 5.

3. Importance of TSA Calculation

Details: Calculating the total surface area is important in geometry, material science, and various engineering applications where the surface properties of this specific polyhedron need to be determined.

4. Using the Calculator

Tips: Enter the edge length in meters. The value must be positive and valid. The calculator will compute the total surface area using the mathematical formula.

5. Frequently Asked Questions (FAQ)

Q1: What is a Rhombic Triacontahedron?
A: A Rhombic Triacontahedron is a convex polyhedron with 30 congruent rhombic faces. It is one of the Catalan solids and is the dual polyhedron of the icosidodecahedron.

Q2: Why is the square root of 5 in the formula?
A: The square root of 5 appears in the formula due to the geometric properties and mathematical relationships inherent in the structure of the Rhombic Triacontahedron.

Q3: What are the practical applications of this calculation?
A: This calculation is used in geometry research, architectural design, material science, and in the study of crystalline structures and polyhedral properties.

Q4: Can this formula be used for any polyhedron?
A: No, this specific formula applies only to the Rhombic Triacontahedron. Different polyhedra have different surface area formulas based on their geometric properties.

Q5: How accurate is this calculation?
A: The calculation is mathematically exact when using precise input values. The result's practical accuracy depends on the precision of the edge length measurement.