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Total Surface Area of Triakis Octahedron Formula:
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The Total Surface Area of a Triakis Octahedron is the total quantity of plane enclosed on the entire surface of this polyhedron. A Triakis Octahedron is an Archimedean dual, or a Catalan solid, with 24 isosceles triangular faces.
The calculator uses the formula:
Where:
Explanation: The formula calculates the total surface area based on the octahedral edge length, incorporating the mathematical constant √2.
Details: Calculating the surface area of geometric solids is crucial in various fields including architecture, material science, and 3D modeling. It helps in determining material requirements, heat transfer properties, and structural characteristics.
Tips: Enter the octahedral edge length in meters. The value must be positive and greater than zero for accurate calculation.
Q1: What is a Triakis Octahedron?
A: A Triakis Octahedron is a Catalan solid that is the dual of the truncated cube. It has 24 faces, 36 edges, and 14 vertices.
Q2: How is this different from a regular octahedron?
A: While both are polyhedra, a regular octahedron has 8 triangular faces, whereas a Triakis Octahedron has 24 isosceles triangular faces.
Q3: What are the practical applications of this calculation?
A: This calculation is used in crystallography, architectural design, and in the study of molecular structures where this specific geometry appears.
Q4: Can this formula be used for any size of Triakis Octahedron?
A: Yes, the formula is scalable and works for any size as long as the proportions of the Triakis Octahedron are maintained.
Q5: Why does the formula contain the constant √2?
A: The √2 constant appears naturally in the geometry of the Triakis Octahedron due to the angles and proportions between its faces and edges.