Truncated Icosidodecahedron Edge of Hexakis Icosahedron given Medium Edge Calculator

Formula Used:

\[ \text{Truncated Edge} = \frac{5}{2 \times \sqrt{15 \times (5 - \sqrt{5})}} \times \frac{22 \times \text{Medium Edge}}{3 \times (4 + \sqrt{5})} \]

Truncated Edge of Hexakis Icosahedron:

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1. What is Truncated Edge of Hexakis Icosahedron?

The Truncated Edge of Hexakis Icosahedron is the length of the edges of a Hexakis Icosahedron that is created by truncating the vertices of an Icosidodecahedron. It represents a specific geometric measurement in this complex polyhedral structure.

2. How Does the Calculator Work?

The calculator uses the mathematical formula:

\[ \text{Truncated Edge} = \frac{5}{2 \times \sqrt{15 \times (5 - \sqrt{5})}} \times \frac{22 \times \text{Medium Edge}}{3 \times (4 + \sqrt{5})} \]

Where:

Medium Edge - The length of the edge that connects two non-adjacent and non-opposite vertices of the Hexakis Icosahedron
√5 - Square root of 5 (approximately 2.23607)

Explanation: This formula calculates the truncated edge length based on the medium edge measurement, using geometric relationships and mathematical constants specific to this polyhedron.

3. Importance of Truncated Edge Calculation

Details: Calculating the truncated edge is important in geometric modeling, architectural design, and mathematical research involving polyhedral structures. It helps in understanding the spatial properties and proportions of complex geometric shapes.

4. Using the Calculator

Tips: Enter the medium edge length in meters. The value must be positive and greater than zero. The calculator will compute the corresponding truncated edge length using the mathematical formula.

5. Frequently Asked Questions (FAQ)

Q1: What is a Hexakis Icosahedron?
A: A Hexakis Icosahedron is a Catalan solid, the dual of the truncated icosahedron, with 120 faces, 180 edges, and 62 vertices.

Q2: What is the relationship between medium edge and truncated edge?
A: The relationship is defined by the specific geometric formula that accounts for the mathematical properties of this polyhedron.

Q3: Can this calculator be used for other polyhedra?
A: No, this calculator is specifically designed for the Hexakis Icosahedron and its truncated edge calculation.

Q4: What units should I use for input?
A: The calculator expects input in meters, but you can use any consistent unit system as the relationship is proportional.

Q5: How accurate is the calculation?
A: The calculation is mathematically precise based on the formula, with results rounded to 6 decimal places for practical use.