Total Surface Area of Tetrakis Hexahedron given Pyramidal Edge Length Calculator

Formula Used:

\[ TSA = \frac{16\sqrt{5}}{3} \times l_{e(Pyramid)}^2 \]

Total Surface Area (TSA):

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1. What is the Tetrakis Hexahedron?

The Tetrakis Hexahedron is a Catalan solid that can be seen as a cube with square pyramids added to each face. It has 24 faces, 36 edges, and 14 vertices.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ TSA = \frac{16\sqrt{5}}{3} \times l_{e(Pyramid)}^2 \]

Where:

\( TSA \) — Total Surface Area of Tetrakis Hexahedron (m²)
\( l_{e(Pyramid)} \) — Pyramidal Edge Length (m)
\( \sqrt{5} \) — Square root of 5 (approximately 2.23607)

Explanation: The formula calculates the total surface area based on the length of the pyramidal edges of the Tetrakis Hexahedron.

3. Importance of Surface Area Calculation

Details: Calculating the surface area of geometric solids is important in various fields including architecture, materials science, and 3D modeling for determining material requirements, heat transfer properties, and structural analysis.

4. Using the Calculator

Tips: Enter the pyramidal edge length in meters. The value must be positive and greater than zero. The calculator will compute the total surface area of the Tetrakis Hexahedron.

5. Frequently Asked Questions (FAQ)

Q1: What is a Tetrakis Hexahedron?
A: A Tetrakis Hexahedron is a Catalan solid that can be derived from a cube by adding square pyramids to each face, resulting in a polyhedron with 24 triangular faces.

Q2: What are the units for the input and output?
A: The pyramidal edge length should be entered in meters (m), and the total surface area will be calculated in square meters (m²).

Q3: Can this calculator handle decimal inputs?
A: Yes, the calculator accepts decimal values for the pyramidal edge length with up to 4 decimal places precision.

Q4: What is the geometric significance of the √5 in the formula?
A: The √5 factor comes from the geometric relationships and trigonometric calculations involved in determining the surface area of the triangular faces of the Tetrakis Hexahedron.

Q5: Are there other ways to calculate the surface area?
A: Yes, the surface area can also be calculated using different parameters such as the edge length of the base cube or the height of the pyramids, but this calculator specifically uses the pyramidal edge length.