The compound of five cuboctahedra is a geometric structure that consists of five cuboctahedra arranged in a specific way. The cuboctahedron is a convex Archimedean solid that has 8 triangular faces and 6 square faces, with 12 edges and 12 vertices. In the context of a compound, the term typically refers to a geometric arrangement where multiple polyhedra share some points or overlap in a way that creates an intricate three-dimensional figure.
The "Compound of Five Great Icosahedra" is a fascinating geometric structure in the realm of polyhedra. It is formed by arranging five great icosahedra (the dual polyhedron of the dodecahedron) around a common center. ### Characteristics: - **Vertices**: The compound has a unique vertex arrangement due to the overlapping and symmetry of the five great icosahedra.
The term "compound of four cubes" refers to a three-dimensional geometric shape constructed by combining four individual cubes in a specific arrangement. This shape can be visualized as each of the four cubes sharing faces with the others, creating a single cohesive structure. One common arrangement for the compound of four cubes is to place the cubes so that they form the shape of a larger cube (specifically, a 2x2x2 cube) when viewed from a certain angle.
The compound of the great icosahedron and the great stellated dodecahedron is known as the "stella octangula" or "octahedral compound." This compound is a three-dimensional figure formed by the intersection of two polyhedra: a great icosahedron (which is one of the Archimedean solids) and a great stellated dodecahedron (a star polyhedron).
The compound of six decagrammic prisms refers to a specific geometric arrangement formed by combining six decagrammic prisms, which are three-dimensional shapes with a decagram (10-sided polygon) as their bases. Each decagrammic prism has two parallel faces that are decagrams and rectangular lateral faces connecting corresponding sides of the two bases. When these six prisms are combined in a specific manner, they can form a three-dimensional structure.
A hexagonal prism is a three-dimensional geometric shape that consists of two parallel hexagonal bases connected by rectangular lateral faces. Here are some key characteristics of a hexagonal prism: 1. **Bases**: The two bases are congruent hexagons (six-sided polygons). 2. **Lateral Faces**: There are six rectangular lateral faces that connect corresponding sides of the two hexagonal bases.
The "Compound of twelve tetrahedra" is a geometric structure composed of twelve tetrahedra arranged in such a way that they intersect and share vertices, edges, and faces, creating a complex arrangement. This compound is notable for its symmetric properties and rotational freedom, meaning that it can be rotated around certain axes while maintaining its overall shape.
The compound of two great dodecahedra is a three-dimensional geometric arrangement in which two great dodecahedra are combined in such a way that they intersect each other. A great dodecahedron is a type of regular polyhedron that is made up of 12 regular pentagonal faces, and it is one of the Archimedean solids. When two great dodecahedra are combined, they can create a fascinating and complex structure.
The compound of two small stellated dodecahedra is a geometric figure formed by the combination of two small stellated dodecahedra, which are both stellated versions of the dodecahedron. The small stellated dodecahedron is a convex polyhedron made up of 12 star-shaped faces, each a pentagram.
The compound of two snub dodecahedra is a geometric structure formed by the intersection of two snub dodecahedra. A snub dodecahedron is a convex Archimedean solid with 12 regular pentagonal faces and 20 triangular faces, featuring a distinct and non-uniform arrangement of vertices and edges. When two snub dodecahedra are combined, they can be positioned in such a way that they intersect.
A decagonal bipyramid is a type of three-dimensional geometric shape that belongs to the family of polyhedra. Specifically, it is a bipyramid based on a decagon, which is a polygon with ten sides. ### Characteristics of a Decagonal Bipyramid: 1. **Base Faces**: The decagonal bipyramid has two decagonal faces as its bases, one at the top and one at the bottom.
A diminished rhombic dodecahedron is a polyhedral shape that is derived from the regular rhombic dodecahedron by truncating its vertices. Essentially, this process involves slicing off the corners of the rhombic dodecahedron, which results in a new figure with more faces.
The elongated pentagonal bipyramid is a type of geometric solid that belongs to the category of polyhedra. It can be described as a bipyramid based on a pentagonal base, with one additional pyramid added to one of its vertices, extending the geometry. ### Characteristics: - **Faces**: The elongated pentagonal bipyramid has 12 faces in total: 5 of the faces are hexagons (from the two base pentagons being connected) and 7 faces are triangles.
A heptagonal antiprism is a type of polyhedron characterized by its two parallel heptagonal (seven-sided) bases and a series of triangular faces connecting the corresponding edges of these bases. In more detail, the heptagonal antiprism has the following properties: - **Faces**: It consists of 9 faces in total - 2 heptagonal faces and 7 triangular lateral faces.
The great disdyakis dodecahedron is a type of convex polyhedron that is part of the broader family of Archimedean solids. Specifically, it is classified as a deltahedra, which means that all of its faces are equilateral triangles. Here are some characteristics of the great disdyakis dodecahedron: 1. **Faces**: It has 120 triangular faces. 2. **Vertices**: There are 60 vertices.
The Great Hexacronic Icositetrahedron, also known as a "great hexacronic icositetrahedron" or "great hexacronic icosahedron," is a type of convex uniform hyperbolic polyhedron. It belongs to the family of polyhedra that can be described using a system of vertices, edges, and faces in higher-dimensional space.
The great icosidodecahedron is a convex Archimedean solid and a type of polyhedron. It is characterized by its unique arrangement of faces, vertices, and edges. Specifically, the great icosidodecahedron has: - **62 faces**: which consist of 20 regular hexagons and 12 regular pentagons. - **120 edges**. - **60 vertices**.
The term "gyrate rhombicosidodecahedron" refers to a specific type of convex polyhedron that is a variation of the rhombicosidodecahedron. A rhombicosidodecahedron is one of the Archimedean solids, characterized by its 62 faces, which include 20 equilateral triangles, 30 squares, and 12 regular pentagons. It has 60 edges and 20 vertices.
A bilge pump is a device used to remove water that has accumulated in the bilge of a boat or ship. The bilge is the lowest compartment of a vessel's hull, where water typically collects due to leaks, waves, or rain. Bilge pumps are essential for maintaining the buoyancy and stability of the vessel, preventing unwanted water from causing damage or capsizing.
Pinned article: Introduction to the OurBigBook Project
Welcome to the OurBigBook Project! Our goal is to create the perfect publishing platform for STEM subjects, and get university-level students to write the best free STEM tutorials ever.
Everyone is welcome to create an account and play with the site: ourbigbook.com/go/register. We belive that students themselves can write amazing tutorials, but teachers are welcome too. You can write about anything you want, it doesn't have to be STEM or even educational. Silly test content is very welcome and you won't be penalized in any way. Just keep it legal!
Intro to OurBigBook
. Source. We have two killer features:
- topics: topics group articles by different users with the same title, e.g. here is the topic for the "Fundamental Theorem of Calculus" ourbigbook.com/go/topic/fundamental-theorem-of-calculusArticles of different users are sorted by upvote within each article page. This feature is a bit like:
- a Wikipedia where each user can have their own version of each article
- a Q&A website like Stack Overflow, where multiple people can give their views on a given topic, and the best ones are sorted by upvote. Except you don't need to wait for someone to ask first, and any topic goes, no matter how narrow or broad
This feature makes it possible for readers to find better explanations of any topic created by other writers. And it allows writers to create an explanation in a place that readers might actually find it.
Figure 1. Screenshot of the "Derivative" topic page. View it live at: ourbigbook.com/go/topic/derivativeVideo 2. OurBigBook Web topics demo. Source. - local editing: you can store all your personal knowledge base content locally in a plaintext markup format that can be edited locally and published either:This way you can be sure that even if OurBigBook.com were to go down one day (which we have no plans to do as it is quite cheap to host!), your content will still be perfectly readable as a static site.
- to OurBigBook.com to get awesome multi-user features like topics and likes
- as HTML files to a static website, which you can host yourself for free on many external providers like GitHub Pages, and remain in full control
Figure 3. Visual Studio Code extension installation.
Figure 4. Visual Studio Code extension tree navigation.
Figure 5. Web editor. You can also edit articles on the Web editor without installing anything locally.Video 3. Edit locally and publish demo. Source. This shows editing OurBigBook Markup and publishing it using the Visual Studio Code extension.Video 4. OurBigBook Visual Studio Code extension editing and navigation demo. Source. 
- Infinitely deep tables of contents:
All our software is open source and hosted at: github.com/ourbigbook/ourbigbook
Further documentation can be found at: docs.ourbigbook.com
Feel free to reach our to us for any help or suggestions: docs.ourbigbook.com/#contact