Medium Edge of Hexakis Octahedron given Insphere Radius Calculator

Formula Used:

\[ l_{Medium} = \frac{3}{7} \times r_i \times \frac{1 + 2\sqrt{2}}{\sqrt{\frac{402 + 195\sqrt{2}}{194}}} \]

Medium Edge of Hexakis Octahedron:

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1. What is Medium Edge of Hexakis Octahedron given Insphere Radius?

The Medium Edge of Hexakis Octahedron given Insphere Radius is the length of the medium edge of any of the congruent triangular faces of the Hexakis Octahedron, calculated based on the radius of the sphere contained within the polyhedron.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ l_{Medium} = \frac{3}{7} \times r_i \times \frac{1 + 2\sqrt{2}}{\sqrt{\frac{402 + 195\sqrt{2}}{194}}} \]

Where:

\( l_{Medium} \) — Medium Edge of Hexakis Octahedron (m)
\( r_i \) — Insphere Radius of Hexakis Octahedron (m)
\( \sqrt{2} \) — Square root of 2 (approximately 1.4142)

Explanation: This formula establishes the mathematical relationship between the insphere radius and the medium edge length of a Hexakis Octahedron, incorporating geometric constants and square root functions.

3. Importance of Medium Edge Calculation

Details: Calculating the medium edge length is essential for understanding the geometric properties of Hexakis Octahedrons, which are important in crystallography, molecular modeling, and architectural design applications.

4. Using the Calculator

Tips: Enter the insphere radius in meters. The value must be positive and greater than zero. The calculator will compute the corresponding medium edge length.

5. Frequently Asked Questions (FAQ)

Q1: What is a Hexakis Octahedron?
A: A Hexakis Octahedron is a Catalan solid that is the dual of the truncated cuboctahedron, featuring 48 congruent triangular faces.

Q2: What is the insphere radius?
A: The insphere radius is the radius of the largest sphere that can be contained within the Hexakis Octahedron, touching all its faces.

Q3: Are there different edge lengths in a Hexakis Octahedron?
A: Yes, a Hexakis Octahedron has three types of edges: short, medium, and long edges, with the medium edge being calculated here.

Q4: What units should I use for input?
A: The calculator uses meters as the unit of measurement. Convert other units to meters before calculation if necessary.

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