1. What is 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 fundamental geometric measurement used in the study of this polyhedron.

2. How Does the Calculator Work?

The calculator uses the formula:

Where:

• \( l_{Base} \) — Base Length of Pentakis Dodecahedron (m)
• \( r_{m} \) — Midsphere Radius of Pentakis Dodecahedron (m)
• \( \sqrt{5} \) — Square root of 5 (approximately 2.23607)

Explanation: This formula calculates the base length of the isosceles triangular face of a Pentakis Dodecahedron based on its midsphere radius.

3. Importance of Base Length Calculation

Details: Calculating the base length is essential for understanding the geometric properties of Pentakis Dodecahedron, including surface area, volume, and other dimensional relationships.

4. Using the Calculator

Tips: Enter the midsphere radius in 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, creating 60 isosceles triangular faces.

Q2: What is the midsphere radius?
A: The midsphere radius is the radius of the sphere that is tangent to all edges of the Pentakis Dodecahedron.

Q3: Why is the square root of 5 in the formula?
A: The square root of 5 appears due to the golden ratio relationship inherent in the geometry of dodecahedron-based polyhedra.

Q4: Can this formula be used for other polyhedra?
A: No, this specific formula applies only to the Pentakis Dodecahedron and its geometric properties.

Q5: How accurate is this calculation?
A: The calculation is mathematically exact when using precise input values, though practical measurements may introduce some error.