Long Edge Of Hexakis Octahedron Given Midsphere Radius Calculator

Formula Used:

\[ l_{Long} = \frac{4 \times r_m}{1 + (2 \times \sqrt{2})} \]

Long Edge (l_Long):

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1. What Is Long Edge Of Hexakis Octahedron Given Midsphere Radius?

The Long Edge of Hexakis Octahedron given Midsphere Radius is the length of the long edge of any of the congruent triangular faces of the Hexakis Octahedron, calculated using the midsphere radius. It helps in understanding the geometric properties of this complex polyhedron.

2. How Does The Calculator Work?

The calculator uses the formula:

\[ l_{Long} = \frac{4 \times r_m}{1 + (2 \times \sqrt{2})} \]

Where:

\( l_{Long} \) — Long Edge of Hexakis Octahedron (m)
\( r_m \) — Midsphere Radius of Hexakis Octahedron (m)
\( \sqrt{2} \) — Square root of 2 (approximately 1.4142)

Explanation: This formula directly relates the midsphere radius to the long edge length through a constant factor derived from the geometric properties of the Hexakis Octahedron.

3. Importance Of Long Edge Calculation

Details: Calculating the long edge is essential for geometric analysis, 3D modeling, and understanding the spatial dimensions of Hexakis Octahedrons in various applications including crystallography and architectural design.

4. Using The Calculator

Tips: Enter the midsphere radius in meters. The value must be positive and valid. The calculator will compute the corresponding long 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 midsphere radius?
A: The midsphere radius is the radius of the sphere that is tangent to all edges of the polyhedron.

Q3: Are there other edges in a Hexakis Octahedron?
A: Yes, Hexakis Octahedrons have both long and short edges, with the long edges being the focus of this calculation.

Q4: What units should I use?
A: The calculator uses meters, but any consistent unit system can be used as long as all measurements are in the same units.

Q5: How accurate is this formula?
A: The formula is mathematically exact for perfect Hexakis Octahedrons and provides precise calculations when accurate inputs are provided.