Whats a tetrahedral number?

Last Update: April 20, 2022

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Asked by: Ms. Harmony Vandervort
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A tetrahedral number, or triangular pyramidal number, is a figurate number that represents a pyramid with a triangular base and three sides, called a tetrahedron.

How do you find the tetrahedral number?

A number is termed as a tetrahedral number if it can be represented as a pyramid with a triangular base and three sides, called a tetrahedron. The nth tetrahedral number is the sum of the first n triangular numbers. The first ten tetrahedral numbers are: 1, 4, 10, 20, 35, 56, 84, 120, 165, 220, …

How many faces has a tetrahedron?

In geometry, a tetrahedron (plural: tetrahedra or tetrahedrons), also known as a triangular pyramid, is a polyhedron composed of four triangular faces, six straight edges, and four vertex corners. The tetrahedron is the simplest of all the ordinary convex polyhedra and the only one that has fewer than 5 faces.

Is 364 a triangle number?

Each “layer” of a tetrahedron is a triangle of dots representing a triangular number: hence each tetrahedron is a sum of triangular numbers. The twelfth tetrahedral number, 364, tells us how many gifts our narrator received in total.

What are Pentelope numbers?

A pentatope number is a number in the fifth cell of any row of Pascal's triangle starting with the 5-term row 1 4 6 4 1, either from left to right or from right to left. The first few numbers of this kind are: 1, 5, 15, 35, 70, 126, 210, 330, 495, 715, 1001, 1365 (sequence A000332 in the OEIS)

Tetrahedral Numbers

36 related questions found

What is a solid triangle called?

In geometry, a solid that is made up of four triangular faces is called tetrahedron. Also, a pyramid that has its base, triangle in shape is called a triangular pyramid. See the diagram below to understand.

What is called tetrahedron?

The regular tetrahedron, often simply called "the" tetrahedron, is the Platonic solid with four polyhedron vertices, six polyhedron edges, and four equivalent equilateral triangular faces, . It is also uniform polyhedron and Wenninger model . It is described by the Schläfli symbol and the Wythoff symbol is. .

How is tetrahedron pronounced?

noun, plural tet·ra·he·drons, tet·ra·he·dra [te-truh-hee-druh].

Is 20 a tetrahedral number?

The tetrahedral numbers are: 1, 4, 10, 20, 35, 56, 84, 120, 165, 220, ... (sequence A000292 in the OEIS)

What is the third hexagonal number?

1, 6, 15, 28, 45, 66, 91, 120, 153, 190, 231, 276, 325, 378, 435, 496, 561, 630, 703, 780, 861, 946...

Which has tetrahedral shape?

Tetrahedral Geometry

Molecules of methane, CH4, ammonia, NH3, and water, H2O, all have four electron groups around their central atom, so they all have a tetrahedral shape and bond angles of about 109.5°.

What is the tetrahedral formula?

The formula to calculate the total surface area of a regular tetrahedron is given as, TSA of Regular Tetrahedron = Sum of 4 congruent equilateral triangles(i.e. lateral faces) TSA of Regular Tetrahedron = 4 ∙ (√3)/4 a2 = √3 a2 square units. where a is the side length of the regular tetrahedron.

What is the next pentagonal number?

1, 5, 12, 22, 35, 51, 70, 92, 117, 145, 176, 210, 247, 287, 330, 376, 425, 477, 532, 590, 651, 715, 782, 852, 925, 1001, 1080, 1162, 1247, 1335, 1426, 1520, 1617, 1717, 1820, 1926, 2035, 2147, 2262, 2380, 2501, 2625, 2752, 2882, 3015, 3151, 3290, 3432, 3577, 3725, 3876, 4030, 4187... (sequence A000326 in the OEIS).

Can a tetrahedron be irregular?

A tetrahedron can also be categorized as regular or irregular. If the four faces of a tetrahedron are equilateral triangles, the tetrahedron is a regular tetrahedron. Otherwise, it is irregular.

What is a double tetrahedron?

In geometry, a compound of two tetrahedra is constructed by two overlapping tetrahedra, usually implied as regular tetrahedra.

What is a 5 sided shape called?

More than Four Sides A five-sided shape is called a pentagon. Interior angle of any regular polygon =180[(n−2)/n] Interior angle of any regular Icosagon = 180(20 - 2)/20 = 162° The sum of all the interior angles of a regular Icosagon is 3240°. A quadrilateral is a four-sided polygon with four angles.

What is a 3D shape?

3D shapes are shapes with three dimensions, such as width, height and depth. An example of a 3D shape is a prism or a sphere. 3D shapes are multidimensional and can be physically held.

What's a 3D triangle?

Triangular Prism (3D shape with identical triangle bases)

What is an example of a Figurate number?

Figurate numbers are numbers that can be represented using geometric shapes. Examples include square, triangle and tetrahedral numbers.

What is the formula for pentagonal numbers?

Each pentagonal number is split into a rectangular array and a triangular number, a subdivision that suggests that we can represent the nth pentagonal number by (n-1)n + Tn, where Tn is the nth triangular number. So the sub-pattern suggests that the nth pentagonal number can be expressed as Pn = (n-1)n + n(n+1)/2.