Since the Euler’s formula does not hold true for the given number of faces, edges and vertices, therefore, there does not exist any polyhedron with 10 faces, 20 edges and 15 vertices.

Hexahedron

Cube

6 faces

Answer: It is a cuboid or quadrilaterally-faced hexahedron.

Answer: No, it cannot have the given. Where F is number of faces, V the number of vertices and E the number of edges. Therefore the polyhedron cannot have the given.

no it can not have .

Answer. Answer: There are 30 edges of a polyhedron having 20 faces and 12 vertices.

Answer. So, it can’t have 10 faces , 20 edges, and 15 vertices.

heptahedron

8

In geometry, a cube is a three-dimensional solid object bounded by six square faces, facets or sides, with three meeting at each vertex. The cube is the only regular hexahedron and is one of the five Platonic solids. It has 6 faces, 12 edges, and 8 vertices.

Vertices of Two-Dimensional Shapes Each point where two straight edges intersect is a vertex. A triangle has three edges – its three sides. It also has three vertices, which are each corner where two edges meet. You can also see from this definition that some two-dimensional shapes do not have any vertices.

3

An edge is where two faces meet. A vertex is a corner where edges meet. The plural is vertices.

square pyramid

A cone is a distinctive three-dimensional geometric figure that has a flat surface and a curved surface, pointed towards the top. The pointed end of the cone is called the apex, whereas the flat surface is called the base.

Pyramids and cones In a pyramid or cone, the apex is the vertex at the “top” (opposite the base).

A cone is a three-dimensional geometric shape that tapers smoothly from a flat base (frequently, though not necessarily, circular) to a point called the apex or vertex.

The frustum is a cone with the top cut off by making a slice parallel to the base. Answers will include a link to the calculation of the full cone. Note that frustum is often misspelled “frustrum.”

If the plane cuts the cone at an angle between these two, such that it maintains contact with the sides of the cone in all locations, then an ellipse is formed (bottom left). If the plane cuts through both cones at a more vertical angle, then the section is a hyperbola.

The curved surface area of frustum of a cone is given by; CSA = πl(R – r) Where r is the radius of upper circle or small circle of frustum and R is the radius large circle or base and l is the slant height.

one frustum

In geometry, a frustum (plural: frusta or frustums) is the portion of a solid (normally a cone or pyramid) that lies between one or two parallel planes cutting it. A right frustum is a parallel truncation of a right pyramid or right cone.

TotalSurface Area of frustum of cone: Total Surface Area (TSA) = pi * l(R + r) + pi(R2 + r2) where r = radius of smaller circle R = radius of bigger circle l = slant height of frustum.

Answer. Height of frustum ( H ) = 16 cm. Radius of top of the frustum ( R ) = 20 cm.

Frustum of a right circular cone is that portion of right circular cone included between the base and a section parallel to the base not passing through the vertex. Properties of Frustum of Right Circular Cone. The altitude of a frustum of a right circular cone is the perpendicular distance between the two bases.

As nouns the difference between frustum and truncation is that frustum is a cone or pyramid whose tip has been truncated by a plane parallel to its base while truncation is the act of truncating or shortening (in all senses).

: the basal part of a solid cone or pyramid formed by cutting off the top by a plane parallel to the base also : the part of a solid intersected between two usually parallel planes.

The slant height of an object (such as a frustum, or pyramid) is the distance measured along a lateral face from the base to the apex along the “center” of the face. In other words, it is the altitude of the triangle comprising a lateral face (Kern and Bland 1948, p. 50).

A right solid is a three dimensional geometric object with a base that is either a circle or a regular polygon. It may come to a point or have a flat top. The flat top must be identical and parallel to the base, and the sides are then perpendicular to them.