An octahedron shape is one which has 8 faces. Since it is a prism it must be a hexagonal prism (2 hexagons and 6 rectangles = 8 faces). And a hexagonal prism has 2*6 = 12 vertices.
1 hexagonal prism = 8 faces (2 hexagons, 6 rectangles), 18 edges, 12 vertices.
Faces: 8 Edges: 18 Vertices: 12 Dual: hexagonal bipyramid Face types: 2 hexagons, 6 rectangles
For all polyhedra: vertices + faces = edges + 2 The given fact is: edges = vertices + 10 → vertices + faces = vertices + 10 + 2 → faces = 12
Faces= 2 edges=5 vertices=12 Faces= 2 edges=5 vertices=12
Each cube has 6 faces, 12 edges and 8 vertices, so two [unconnected] cubes have 12 faces, 24 edges and 16 vertices (between them).
Here is some information about the 13 Archimedean solids:Tetrahedron-related:1) The truncated tetrahedron has 12 vertices, 18 edges, & 8 faces (4 triangles & 4 hexagons).Cube-related:2) The truncated cube has 24 vertices, 36 edges, & 14 faces (8 triangles & 6 octagons). Also known as a truncated hexahedron.3) The truncated octahedron has 24 vertices, 36 edges, & 14 faces (6 squares & 8 hexagons).4) The cuboctahedron has 12 verticies, 24 edges, & 14 faces (8 triangles & 6 squares).5) The small rhombicuboctahedron has 24 vertices, 48 edges, & 26 faces (8 triangles & 18 squares). Also known simply as a rhombicuboctahedron.6) The great rhombicuboctahedron has 48 vertices, 72 edges, & 26 faces (12 squares, 8 hexagons, & 6 octagons). Also known as a truncated cuboctahedron.7) The snub cube has 24 vertices, 60 edges, & 38 faces (32 triangles & 6 squares). Also known variously as a snub hexahedron, snub octahedron, or snub cuboctahedron. This shape, along with the snub dodecahedron, has 2 chiral forms.Icosahedron-related:8) The truncated icosahedron has 60 vertices, 90 edges, & 32 faces (12 pentagons & 20 hexagons). Also known as a buckyball or a football/soccer ball.9) The truncated dodecahedron has 60 vertices, 90 edges, & 32 faces (20 triangles & 12 decagons).10) The icosidodecahedron has 30 vertices, 60 edges, & 32 faces (20 triangles & 12 pentagons).11) The small rhombicosidodecahedron has 60 vertices, 120 edges, & 62 faces (20 triangles, 30 squares, & 12 pentagons). Also known simply as a rhombicosidodecahedron.12) The great rhombicosidodecahedron has 120 vertices, 180 edges, & 62 faces (30 squares, 20 hexagons, & 12 decagons). Also known as a truncated icosidodecahedron.13) The snub dodecahedron has 60 vertices, 150 edges, & 92 faces (80 triangles & 12 pentagons). Also known as a snub icosahedron or a snub icosidodecahedron. This shape, along with the snub cube, has 2 chiral forms.
faces= 10 vertices-=26 edges=17 * * * * * Wrong on each count! Faces: 8 Edges: 18 Vertices: 12
Faces + Vertices = Edges + 2 This is called Euler's formula. For example a cube has 8 vertices, 6 faces and 12 edges so: 6 + 8 = 12 + 2 14 = 14 The formula works.
12 faces on a truncated icosahedron are pentagons. (The other 20 faces are hexagons.)
A prism with an n-sided base will have 2n vertices, n + 2 faces, and 3n edges. 12 faces
A prism with an n-sided base will have 2n vertices, n + 2 faces, and 3n edges. 6 faces, 8 vertices, 12 edges.