Formula Used:
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The height of a Triakis Tetrahedron given its insphere radius is the vertical distance from any vertex to the opposite face, calculated using the specific geometric relationship between these two properties of the polyhedron.
The calculator uses the formula:
Where:
Explanation: This formula establishes the precise mathematical relationship between the height of a Triakis Tetrahedron and the radius of its inscribed sphere, derived from the geometric properties of this specific polyhedron.
Details: Calculating the height of a Triakis Tetrahedron is essential for understanding its spatial dimensions, volume calculations, and for applications in geometry, architecture, and material science where this specific polyhedral shape is used.
Tips: Enter the insphere radius in meters. The value must be positive and valid (radius > 0). The calculator will compute the corresponding height of the Triakis Tetrahedron.
Q1: What is a Triakis Tetrahedron?
A: A Triakis Tetrahedron is a Catalan solid that can be seen as a tetrahedron with triangular pyramids added to each face.
Q2: Why is there a square root of 33 in the formula?
A: The √33 term comes from the specific geometric relationships and proportions inherent to the Triakis Tetrahedron's structure.
Q3: Can this formula be used for any polyhedron?
A: No, this specific formula applies only to Triakis Tetrahedrons due to their unique geometric properties.
Q4: What are practical applications of this calculation?
A: This calculation is useful in crystallography, architectural design, and mathematical modeling where Triakis Tetrahedron shapes are employed.
Q5: How accurate is this formula?
A: The formula is mathematically exact for ideal Triakis Tetrahedrons and provides precise results when correct measurements are input.