Symmetry Diagonal Of Deltoidal Icositetrahedron Given Short Edge Calculator

Formula Used:

\[ d_{Symmetry} = \frac{\sqrt{46 + 15\sqrt{2}}}{7} \times \frac{7 \times l_{e(Short)}}{4 + \sqrt{2}} \]

Symmetry Diagonal of Deltoidal Icositetrahedron:

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1. What is the Symmetry Diagonal of Deltoidal Icositetrahedron?

The Symmetry Diagonal of Deltoidal Icositetrahedron is the diagonal which cuts the deltoid faces of Deltoidal Icositetrahedron into two equal halves. It's an important geometric property of this polyhedron.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ d_{Symmetry} = \frac{\sqrt{46 + 15\sqrt{2}}}{7} \times \frac{7 \times l_{e(Short)}}{4 + \sqrt{2}} \]

Where:

\( d_{Symmetry} \) — Symmetry Diagonal of Deltoidal Icositetrahedron (m)
\( l_{e(Short)} \) — Short Edge of Deltoidal Icositetrahedron (m)
\( \sqrt{2} \) — Square root of 2 (approximately 1.4142)

Explanation: This formula calculates the symmetry diagonal based on the short edge length of the deltoidal faces, incorporating the mathematical constant √2.

3. Importance of Symmetry Diagonal Calculation

Details: Calculating the symmetry diagonal is crucial for understanding the geometric properties of the Deltoidal Icositetrahedron, including its symmetry characteristics and spatial relationships between different elements of the polyhedron.

4. Using the Calculator

Tips: Enter the short edge length of the Deltoidal Icositetrahedron in meters. The value must be positive and greater than zero.

5. Frequently Asked Questions (FAQ)

Q1: What is a Deltoidal Icositetrahedron?
A: A Deltoidal Icositetrahedron is a Catalan solid with 24 deltoid (kite-shaped) faces. It is the dual polyhedron of the rhombicuboctahedron.

Q2: How is the symmetry diagonal different from other diagonals?
A: The symmetry diagonal specifically refers to the diagonal that bisects the deltoid faces symmetrically, creating two equal halves of each face.

Q3: What are the practical applications of this calculation?
A: This calculation is primarily used in geometry, crystallography, and architectural design where precise polyhedral measurements are required.

Q4: Can this formula be used for other polyhedra?
A: No, this specific formula applies only to the Deltoidal Icositetrahedron due to its unique geometric properties.

Q5: What units should be used for input and output?
A: The calculator uses meters for both input (short edge) and output (symmetry diagonal), but the formula works with any consistent unit of length.