1. What is the Edge Length of Truncated Icosidodecahedron?

The edge length of a truncated icosidodecahedron is the length of any edge of this Archimedean solid. It is a uniform polyhedron with 62 faces: 30 squares, 20 regular hexagons, and 12 regular decagons.

2. How Does the Calculator Work?

The calculator uses the formula:

Where:

• \( l_e \) — Edge Length of Truncated Icosidodecahedron (m)
• \( r_c \) — Circumsphere Radius of Truncated Icosidodecahedron (m)

Explanation: This formula relates the edge length of a truncated icosidodecahedron to the radius of its circumscribed sphere, using the mathematical constant √5.

3. Importance of Edge Length Calculation

Details: Calculating the edge length is essential for geometric analysis, 3D modeling, architectural design, and understanding the properties of this complex polyhedron.

4. Using the Calculator

Tips: Enter the circumsphere radius in meters. The value must be positive and greater than zero for accurate calculation.

5. Frequently Asked Questions (FAQ)

Q1: What is a truncated icosidodecahedron?
A: It's an Archimedean solid created by truncating both the icosahedron and dodecahedron, resulting in a polyhedron with 62 faces.

Q2: What are the applications of this calculation?
A: This calculation is used in mathematics education, 3D computer graphics, architectural design, and geometric modeling.

Q3: How accurate is this formula?
A: The formula is mathematically exact and provides precise results when correct input values are used.

Q4: Can this calculator handle different units?
A: The calculator uses meters as the default unit. For other units, convert your measurement to meters before input.

Q5: What is the significance of the √5 constant in the formula?
A: √5 appears in the formula due to the golden ratio relationship inherent in the geometry of the icosidodecahedron and its truncated form.