1. What is Base Length of Pentakis Dodecahedron?

The Base Length of Pentakis Dodecahedron refers to the length of the base of the isosceles triangular faces that form the Pentakis Dodecahedron, a Catalan solid derived from the dodecahedron by placing a pyramid on each face.

2. How Does the Calculator Work?

The calculator uses the formula:

Where:

• \( l_{Base} \) — Base Length of Pentakis Dodecahedron (m)
• \( r_i \) — Insphere Radius of Pentakis Dodecahedron (m)

Explanation: This formula calculates the base length from the insphere radius using the geometric properties of the Pentakis Dodecahedron.

3. Importance of Base Length Calculation

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

4. Using the Calculator

Tips: Enter the insphere radius 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 with 60 isosceles triangular faces, derived from the dodecahedron by placing a pyramid on each of its faces.

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

Q3: Are there other ways to calculate the base length?
A: Yes, the base length can also be calculated from other parameters such as the total surface area, volume, or midsphere radius.

Q4: What are the units for base length?
A: The base length is typically measured in meters (m), but any consistent unit of length can be used.

Q5: Is this formula accurate for all Pentakis Dodecahedrons?
A: Yes, this formula is derived from the geometric properties and is accurate for all regular Pentakis Dodecahedrons.