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A space-filling polyhedron, also known as a tessellating polyhedron, is a three-dimensional geometric shape that can fill space without gaps or overlaps when repeated. Essentially, when these polyhedra are arranged in a lattice or grid formation, they completely fill a volume without leaving any empty spaces. The most common example of a space-filling polyhedron is the cube, which can tile three-dimensional space perfectly.

Sphenocorona is a genus of plants in the family Cyclanthaceae. It is composed of flowering plants known for their unique morphological features and relatively limited distribution. Members of this genus are primarily found in tropical regions, particularly in Central and South America. The term "Sphenocorona" itself is derived from Greek roots, where "spheno" refers to a wedge shape and "corona" can mean crown or halo, reflecting some characteristic of the plant's structure.

Sphenomegacorona is a term that does not appear to be widely recognized in established scientific literature or common terminology. As of my last update in October 2023, it is possible that it could refer to a newly discovered species, classification, or concept in a specific field, such as biology, paleontology, or even an entirely different context.

A square bifrustum is a three-dimensional geometric shape, typically associated with the field of geometry, particularly in the study of polyhedra. It can be understood as a variation of a frustum, which is a portion of a solid (usually a cone or a pyramid) that lies between two parallel planes cutting through it.

A square cupola is a type of polyhedral structure that is classified as one of the Archimedean solids. It is formed by taking a square base and extending its sides upward to form a dome-like shape with a single vertex above the center of the base. The square cupola consists of: - A square base. - Eight triangular faces that slope upwards from the sides of the square base to meet at a single apex (the top point of the cupola).

A square gyrobicupola is a type of geometric solid that belongs to the category of Archimedean solids. More specifically, it is a type of polyhedron characterized by its unique combination of square faces and triangular faces.

A square orthobicupola is a type of polyhedron that belongs to the category of Archimedean solids. Specifically, it is formed by the combination of two square cupolas and has a unique geometric configuration. ### Features of the Square Orthobicupola: 1. **Faces**: The square orthobicupola has a total of 24 faces. These consist of: - 8 square faces - 16 triangular faces 2.

The stellated truncated hexahedron, also known as the "snub cuboctahedron," is a type of Archimedean solid. It belongs to a family of geometric shapes known for having regular polygons as faces and being vertex-transitive, meaning that each vertex has the same structure around it. ### Properties of the Stellated Truncated Hexahedron: 1. **Faces**: It has a total of 38 faces.

A tetragonal trapezohedron is a type of polyhedron that has 14 faces, all of which are kite-shaped. It belongs to the family of convex polyhedra and can be categorized as a type of trapezohedron specifically defined by its geometry. Key characteristics of a tetragonal trapezohedron include: 1. **Faces**: It has 14 faces that are all kites. This means each face has two pairs of adjacent sides that are equal in length.

The tetrakis cuboctahedron is a polyhedral structure that is derived from the cuboctahedron, which is a convex Archimedean solid. The cuboctahedron is characterized by having 8 triangular faces and 6 square faces, with a total of 12 edges and 12 vertices. To form the tetrakis cuboctahedron, each face of the cuboctahedron is subdivided such that pyramids are placed on its faces.

The trapezo-rhombic dodecahedron is a type of convex polyhedron that belongs to the category of Archimedean solids. It is characterized by having 12 faces, which are a mix of trapezoids and rhombuses. Specifically, there are 6 trapezoidal faces and 6 rhombic faces.

The Triakis octahedron is a convex polyhedron that can be classified as a type of Archimedean solid. It is derived from the regular octahedron by adding a pyramid to each face of the octahedron, where each pyramid has a triangular base. This construction results in a solid that retains the overall symmetry of the octahedron but has additional vertices, edges, and faces.

A triakis tetrahedron is a type of polyhedron that can be considered a variation of a tetrahedron. Specifically, it is formed by taking a regular tetrahedron and adding a triangular pyramid (or tetrahedral apex) to each of the faces of the original tetrahedron. The key characteristics of a triakis tetrahedron include: 1. **Vertices, Edges, and Faces**: The triakis tetrahedron has 12 edges, 8 faces, and 4 vertices.

The triakis truncated tetrahedron is a type of Archimedean solid. It is a geometric shape that can be constructed by taking a regular tetrahedron (which has four triangular faces) and truncating (slicing off) each of its vertices.

A triangular bifrustum is a three-dimensional geometric shape that is essentially formed by truncating the top and bottom of a triangular prism. Specifically, it consists of two parallel triangular bases—one larger than the other—and three rectangular lateral faces that connect the corresponding sides of the two triangular bases.

A triangular cupola is a type of geometric shape categorized as a polyhedron. It is part of a family of shapes known as cupolas, which are constructed by connecting two bases—one being a polygon and the other a similar polygon that is either translated or shifted vertically. In the case of a triangular cupola, the two bases are triangles.

A triangular hebesphenorotunda is a type of convex polyhedron, which belongs to a specific category of Archimedean solids. To understand it better, it can be described as a truncated version of a triangular prism combined with the properties of other geometric shapes. Here's a breakdown of the name: - **Triangular:** This refers to the shape of the base, specifically that it is a triangle.

The triangular orthobicupola is a type of Archimedean solid that is composed of two triangular cupolae (also known as "cupolas") joined at their bases, with a symmetry that allows for triangular and square faces. It is characterized by its geometry, which features: - **Vertices**: It has 24 vertices. - **Edges**: The solid consists of 36 edges.

The triaugmented dodecahedron is a geometric shape that is categorized as an Archimedean solid. It is formed by augmenting a regular dodecahedron (which has 12 faces, each a regular pentagon) with three additional pyramidal structures.

A triaugmented hexagonal prism is a type of geometric solid that belongs to the family of solids known as "augmented prisms." This specific prism is obtained by taking a standard hexagonal prism and augmenting it with additional pyramid-like shapes (called "augmented" shapes) on each of the two hexagonal bases.