Octahedral number
An octahedral number is a way to count things like building blocks in a structure. Imagine having a set of blocks that can fit together to create a big cube shape. If you count how many blocks are needed to make a single layer of the cube, it would be a square number (like 1, 4, 9, 16, etc.).
But if you count how many blocks are needed to make two layers on top of each other, it would be an octahedral number. This is because the cube has eight corners, and if you imagine lines connecting those corners to form two 4-sided pyramids, you get an octahedron shape.
So an octahedral number is basically a way to count the number of blocks needed to create that shape. It goes like this: 1, 6, 19, 44, 85, and so on. Each number is the sum of the previous octahedral number and three times the square of the counting number (like 1, 2, 3, 4, etc.).
Overall, an octahedral number is just a fancy way to count the building blocks needed for a certain structure, specifically one that looks like two 4-sided pyramids connected at the base.
But if you count how many blocks are needed to make two layers on top of each other, it would be an octahedral number. This is because the cube has eight corners, and if you imagine lines connecting those corners to form two 4-sided pyramids, you get an octahedron shape.
So an octahedral number is basically a way to count the number of blocks needed to create that shape. It goes like this: 1, 6, 19, 44, 85, and so on. Each number is the sum of the previous octahedral number and three times the square of the counting number (like 1, 2, 3, 4, etc.).
Overall, an octahedral number is just a fancy way to count the building blocks needed for a certain structure, specifically one that looks like two 4-sided pyramids connected at the base.