Short Edge Of Hexakis Octahedron Given Truncated Cuboctahedron Edge Calculator

Formula Used:

\[ \text{Short Edge} = \frac{2}{7} \times \sqrt{30 - 3\sqrt{2}} \times \text{Truncated Cuboctahedron Edge} \]

Short Edge of Hexakis Octahedron:

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1. What is the Short Edge of Hexakis Octahedron?

The Short Edge of Hexakis Octahedron is the length of the shortest edge of any of the congruent triangular faces of the Hexakis Octahedron. It is an important geometric measurement in polyhedral studies.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ \text{Short Edge} = \frac{2}{7} \times \sqrt{30 - 3\sqrt{2}} \times \text{Truncated Cuboctahedron Edge} \]

Where:

Truncated Cuboctahedron Edge — The length of the edges of a Hexakis Octahedron created by truncating the vertices of a Cuboctahedron (in meters)

Explanation: The formula calculates the shortest edge length of a Hexakis Octahedron based on its relationship with a truncated cuboctahedron edge.

3. Importance of Short Edge Calculation

Details: Accurate calculation of the short edge is crucial for geometric modeling, architectural design, and understanding the properties of complex polyhedra in mathematics and engineering applications.

4. Using the Calculator

Tips: Enter the truncated cuboctahedron edge length in meters. The value must be positive and greater than zero.

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: How is this different from a regular octahedron?
A: While both are polyhedra, a Hexakis Octahedron has many more faces (48) compared to a regular octahedron (8), and its faces are isosceles triangles rather than equilateral triangles.

Q3: What are practical applications of this calculation?
A: This calculation is used in crystallography, architectural design, 3D modeling, and mathematical research involving polyhedral geometry.

Q4: Can this formula be used for any Hexakis Octahedron?
A: Yes, this formula applies to all Hexakis Octahedra as it describes the fundamental relationship between the short edge and the truncated cuboctahedron edge.

Q5: What precision should I use for the input?
A: For most applications, 4-6 decimal places of precision are sufficient, though the calculator can handle higher precision if needed.