1. What is the Total Surface Area of Pentakis Dodecahedron?

The Total Surface Area of Pentakis Dodecahedron is the amount or quantity of two dimensional space covered on the surface of Pentakis Dodecahedron. It represents the sum of the areas of all the faces of this geometric solid.

2. How Does the Calculator Work?

The calculator uses the formula:

Where:

• \( TSA \) — Total Surface Area of Pentakis Dodecahedron (m²)
• \( l_{Base} \) — Base Length of Pentakis Dodecahedron (m)

Explanation: The formula calculates the total surface area by squaring the base length, multiplying by the constant fraction 15/19, and then multiplying by the square root of the expression (413 + 162√5).

3. Importance of Total Surface Area Calculation

Details: Calculating the total surface area is crucial for various applications including material estimation, structural analysis, and geometric modeling of Pentakis Dodecahedron shapes.

4. Using the Calculator

Tips: Enter the base length of the Pentakis Dodecahedron in meters. The value must be positive and greater than zero.

5. Frequently Asked Questions (FAQ)

Q1: What is a Pentakis Dodecahedron?
A: A Pentakis Dodecahedron is a Catalan solid that is the dual of the truncated icosahedron. It has 60 isosceles triangular faces.

Q2: What units should I use for the base length?
A: The base length should be entered in meters, but the formula works with any consistent unit system (the result will be in square units of the input).

Q3: Can this calculator handle decimal inputs?
A: Yes, the calculator accepts decimal values for more precise calculations.

Q4: What is the significance of the constants in the formula?
A: The constants 15/19 and the expression under the square root are derived from the geometric properties and trigonometric relationships of the Pentakis Dodecahedron.

Q5: How accurate is the calculated result?
A: The result is accurate to 6 decimal places, which is sufficient for most practical applications involving surface area calculations.