Formula Used:
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The Total Surface Area of a Pentakis Dodecahedron is the total area of all its faces. A Pentakis Dodecahedron is a Catalan solid that is the dual of the truncated icosahedron, featuring 60 isosceles triangular faces.
The calculator uses the formula:
Where:
Explanation: The formula calculates the total surface area based on the insphere radius, incorporating mathematical constants and geometric relationships specific to the Pentakis Dodecahedron.
Details: Calculating the total surface area is crucial for various applications in geometry, material science, and engineering, especially when dealing with the properties and behavior of polyhedral structures.
Tips: Enter the insphere radius in meters. The value must be positive and greater than zero to compute the total surface area accurately.
Q1: What is a Pentakis Dodecahedron?
A: A Pentakis Dodecahedron is a Catalan solid with 60 faces, each being an isosceles triangle. It is the dual of the truncated icosahedron.
Q2: How is the insphere radius defined?
A: The insphere radius is the radius of the largest sphere that can fit inside the Pentakis Dodecahedron, touching all its faces.
Q3: What units should be used for input?
A: The input for insphere radius should be in meters (m), and the output total surface area will be in square meters (m²).
Q4: Are there limitations to this formula?
A: This formula is specific to the Pentakis Dodecahedron and assumes ideal geometric conditions. It may not apply to modified or irregular shapes.
Q5: Can this calculator be used for other polyhedra?
A: No, this calculator is specifically designed for the Pentakis Dodecahedron. Other polyhedra require different formulas for surface area calculation.