1. What is the Base Length of Pentakis Dodecahedron?

The Base Length of Pentakis Dodecahedron is the length of the base of the isosceles triangular face of Pentakis Dodecahedron. It is a crucial measurement in understanding the geometry and properties of this polyhedron.

2. How Does the Calculator Work?

The calculator uses the formula:

Where:

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

Explanation: This formula derives the base length from the total surface area using mathematical relationships specific to the Pentakis Dodecahedron geometry.

3. Importance of Base Length Calculation

Details: Calculating the base length is essential for understanding the dimensional properties of Pentakis Dodecahedron, which has applications in various fields including crystallography, architecture, and mathematical modeling.

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 Pentakis Dodecahedron?
A: A Pentakis Dodecahedron is a Catalan solid that can be seen as a dodecahedron with a pyramid on each face.

Q2: What are the units for base length?
A: The base length is typically measured in meters (m), consistent with the input surface area units.

Q3: Can this calculator handle different units?
A: The calculator expects input in square meters. Convert other units to square meters before calculation.

Q4: What is the precision of the calculation?
A: The result is rounded to 10 decimal places for practical use while maintaining mathematical accuracy.

Q5: Are there limitations to this formula?
A: This formula is specifically designed for Pentakis Dodecahedron and assumes ideal geometric conditions.