One of these two crossings is visible in the stellated octahedron the other crossing occurs at a point at infinity of the projective space, between two parallel edges of the two tetrahedra. The two tetrahedra of the compound view of the stellated octahedron are 'desmic', meaning that (when interpreted as a line in projective space) each edge of one tetrahedron crosses two opposite edges of the other tetrahedron.
The stellated octahedron is the first iteration of the 3D analogue of a Koch snowflake.Ī compound of two spherical tetrahedra can be constructed, as illustrated. It can be seen as a net of a four-dimensional octahedral pyramid, consisting of a central octahedron surrounded by eight tetrahedra.Ī single diagonal triangle facetting in red.It can be seen as a being a tetragram, a compound of two dual digons, and the tetrahedron seen as a digonal antiprism, this can be seen as a compound of two digonal antiprisms.It is a facetting of the cube, sharing the vertex arrangement.In this construction it has the same topology as the convex Catalan solid, the triakis octahedron, which has much shorter pyramids. It can be obtained as an augmentation of the regular octahedron, by adding tetrahedral pyramids on each face.It is also a regular polyhedron compound, when constructed as the union of two regular tetrahedra (a regular tetrahedron and its dual tetrahedron).The only stellation of a regular octahedron, with one stellation plane in yellow. It is a stellation of the regular octahedron, sharing the same face planes.The stellated octahedron can be constructed in several ways: The first stage of the construction of the Koch Snowflake is a single central tetrahedron, and the second stage, formed by adding four smaller tetrahedra to the faces of the central tetrahedron, is the stellated octahedron. It can also be seen as one of the stages in the construction of a 3D Koch snowflake, a fractal shape formed by repeated attachment of smaller tetrahedra to each triangular face of a larger figure.
This can be generalized to any desired amount of higher dimensions the four-dimensional equivalent construction is the compound of two 5-cells. It can be seen as a 3D extension of the hexagram: the hexagram is a two-dimensional shape formed from two overlapping equilateral triangles, centrally symmetric to each other, and in the same way the stellated octahedron can be formed from two centrally symmetric overlapping tetrahedra. It is also the least dense of the regular polyhedral compounds, having a density of 2.
It is the simplest of five regular polyhedral compounds, and the only regular compound of two tetrahedra. It was depicted in Pacioli's De Divina Proportione, 1509. It is also called the stella octangula (Latin for 'eight-pointed star'), a name given to it by Johannes Kepler in 1609, though it was known to earlier geometers. The stellated octahedron is the only stellation of the octahedron. Seen as a compound of two regular tetrahedra (red and yellow) On one side hangs the yellow, mid-length, and on the other side is the blue, the highest of all.(Redirected from Star Tetrahedron) Stellated octahedron Here the red hangs the lowest, in the middle. You can have the octahedra in the same size but hung in ascending order. With its geometrical shapes and the precise Mathematical relationship between the elements the mobile provides your baby with their first STEM (Science, Technology, Engineering, Mathematics) experience.By offering images that babies find extremely attractive, it encourages focus and concentration, starting the foundation for their cognitive development.Encourages switching their gaze between objects.Dynamic visual tracking – being able to follow a moving object.Binocularity – the two eyes working together.It strengthens the muscles in the eyes, neck, arms and even core muscles.It develops their eyesight with age-appropriate stimulus.
WHAT ARE THE SCIENTIFIC BENEFITS OF THE OCTAHEDRON MOBILE? As a result, they attract babies’ attention for a sustained period of time. The shiny, metallic paper can easily catch and reflect the light. The elements are very lightweight, therefore they swing gently in the slightest air current. As babies’ sight slowly develops, this mobile provides an ongoing interest for their eyes. Then comes the yellow, middle-size, and finally the blue, the smallest of them. The strong colours of the octahedra are simply fascinating for newborns! Red is the most visible colour for them, this would be the biggest element. SO WHY IS THE MONTESSORI OCTAHEDRON MOBILE SO ATTRACTIVE FOR YOUR BABY?
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