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The Truncated Cuboctahedron Edge of Hexakis Octahedron is the length of the edges of a Hexakis Octahedron that is created by truncating the vertices of a Cuboctahedron. This geometric transformation creates a polyhedron with specific edge length relationships.
The calculator uses the mathematical formula:
Where:
Explanation: This formula calculates the truncated cuboctahedron edge length based on the medium edge length of the hexakis octahedron, using specific geometric constants and mathematical operations.
Details: This calculation is important in geometric modeling, architectural design, and mathematical studies of polyhedra. It helps in understanding the relationships between different edge lengths in complex geometric structures.
Tips: Enter the medium edge length in meters. The value must be positive and valid. The calculator will compute the corresponding truncated cuboctahedron edge length.
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 significance of the constants in the formula?
A: The constants \(\frac{7}{3}\) and \(\sqrt{12 + 6\sqrt{2}}\) are derived from the geometric properties and mathematical relationships between the truncated cuboctahedron and the hexakis octahedron.
Q3: Can this calculator be used for other polyhedra?
A: No, this specific formula and calculator are designed specifically for the relationship between the truncated cuboctahedron edge and medium edge of hexakis octahedron.
Q4: What precision should I expect from the calculation?
A: The calculator provides results with 6 decimal places precision, which is suitable for most geometric and mathematical applications.
Q5: Are there any limitations to this calculation?
A: The calculation assumes perfect geometric forms and may not account for manufacturing tolerances or material properties in practical applications.