Height of Triakis Tetrahedron given Midsphere Radius Calculator

Formula:

\[ h = \frac{6}{5} \times \sqrt{12} \times r_m \]

Height of Triakis Tetrahedron:

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1. What is the Height of Triakis Tetrahedron?

The height of a Triakis Tetrahedron is the vertical distance from any vertex to the face directly opposite to that vertex. It's an important geometric measurement that helps characterize the three-dimensional shape of this polyhedron.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ h = \frac{6}{5} \times \sqrt{12} \times r_m \]

Where:

\( h \) — Height of Triakis Tetrahedron (m)
\( r_m \) — Midsphere Radius of Triakis Tetrahedron (m)

Explanation: The formula establishes a direct relationship between the height of the Triakis Tetrahedron and its midsphere radius, using a constant multiplier derived from the geometric properties of the shape.

3. Importance of Height Calculation

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 form is utilized.

4. Using the Calculator

Tips: Enter the midsphere radius in meters. The value must be positive and non-zero. The calculator will compute the corresponding height of the Triakis Tetrahedron.

5. Frequently Asked Questions (FAQ)

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. It has 12 isosceles triangular faces.

Q2: What is the midsphere radius?
A: The midsphere radius is the radius of a sphere that is tangent to all edges of the polyhedron.

Q3: Can this formula be used for any Triakis Tetrahedron?
A: Yes, this formula applies to all regular Triakis Tetrahedra, where all triangular pyramids added to the base tetrahedron are congruent.

Q4: What are the units of measurement?
A: The calculator uses meters for both input and output, but any consistent unit of length can be used as long as it's the same for both values.

Q5: How accurate is this calculation?
A: The calculation is mathematically exact based on the geometric properties of the Triakis Tetrahedron, limited only by the precision of the input value and computational rounding.