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The numbers in the question are not consistent with the Euler characteristic and therefore there is no simply connected polyhedron that meets these requirements.

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Q: What shape has 8 faces 13 edges and 6 vertices?
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What is a 13 faced 3D shape called?

Gyroelongated square pyramid, It contains 13 faces, 9 vertices and 20 edges. Please, go to the link provided below the answer, to its figure.


What are the characteristics of the Archimedean solids?

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.


What is the sum of the number of vertices and edges of a rectangular pyramid?

13


What is the Name of shape with 13 edges?

Triskaidecagon


How many vertexes does a network with 13 edges have?

It depends on the shape. The number of edges, alone, is not enough to determine a unique shape.