Printable PDF 3D Shapes Worksheets | Cazoom Maths - Free Printable

Let’s go step by step to name each 3D shape and count its vertices, faces, and edges.

We’ll use simple rules:
- Vertices = corners (points where edges meet)
- Faces = flat or curved surfaces
- Edges = lines where two faces meet

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Shape 1: Rectangular Prism (like a box)

- Name: Rectangular prism
- Vertices: 8 (corners of the box)
- Faces: 6 (top, bottom, front, back, left, right)
- Edges: 12 (each side has 4 edges, but shared — total 12)

✔ Check: Euler’s formula for polyhedra: V - E + F = 2 → 8 - 12 + 6 = 2 ✔️

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Shape 2: Triangular Prism (has triangle bases)

- Name: Triangular prism
- Vertices: 6 (3 on top triangle, 3 on bottom)
- Faces: 5 (2 triangles + 3 rectangles)
- Edges: 9 (3 on top, 3 on bottom, 3 connecting them)

✔ Check: 6 - 9 + 5 = 2 ✔️

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Shape 3: Cone

- Name: Cone
- Vertices: 1 (the point at the top — apex)
- Faces: 2 (1 circular base + 1 curved surface)
- Edges: 1 (where the curved surface meets the base — it’s a circle, so one continuous edge)

⚠️ Note: Some curricula say cone has 0 edges because the base is curved — but in most elementary math, we count the circular boundary as 1 edge. We’ll go with 1 edge here since that’s common in K-8.

Actually — let’s double-check standard school definition:
In many textbooks (especially US Common Core), a cone is said to have:
- 1 vertex (apex)
- 1 face (the curved surface) — sometimes they don’t count the base as a “face” if it’s not flat? Wait no — actually, the base IS a flat face.

Standard answer for elementary level:
→ Cone: 1 vertex, 2 faces (base + curved), 1 edge (circular rim)

But wait — some sources say cone has 0 edges because edges are straight lines. This is confusing.

Let me check reliable source: In K-8 geometry, often:
- Cone: 1 vertex, 2 faces, 0 edges? Or 1 edge?

Actually, looking at typical worksheets like this one — they usually accept:
→ Cone: 1 vertex, 2 faces, 1 edge (the circular base edge)

I think for consistency with this worksheet’s level, we’ll use:
Name: Cone
Vertices: 1
Faces: 2
Edges: 1

(If your teacher says differently, follow their rule — but this is common.)

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Shape 4: Square Pyramid (pyramid with square base)

- Name: Square pyramid
- Vertices: 5 (4 around base + 1 apex)
- Faces: 5 (1 square base + 4 triangular sides)
- Edges: 8 (4 around base + 4 from base to apex)

✔ Check: 5 - 8 + 5 = 2 ✔️

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Shape 5: Cylinder

- Name: Cylinder
- Vertices: 0 (no corners)
- Faces: 3? Wait — 2 flat circles (top and bottom) + 1 curved surface → so 3 faces?
BUT — again, in elementary math, sometimes they say cylinder has 2 faces (only the curved part?) — no.

Standard elementary answer:
→ Cylinder: 0 vertices, 2 faces (the two circular bases), 0 edges? Or 2 edges?

Wait — confusion again.

Actually, in most K-8 curricula:
- Cylinder: 0 vertices, 2 faces (top and bottom circles), 0 edges — because edges must be straight lines, and the sides are curved.

But some say 2 edges (the two circular rims).

Looking at similar worksheets — they often say:
Cylinder: 0 vertices, 2 faces, 0 edges

Why? Because "edges" are defined as straight line segments where two flat faces meet. Since the curved surface isn't flat, and the circles aren't made of straight lines, no edges.

So let’s go with:
Name: Cylinder
Vertices: 0
Faces: 2 (the two circular ends)
Edges: 0

This matches what’s taught in many schools for this level.

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Shape 6: Cube (special rectangular prism)

- Name: Cube
- Vertices: 8
- Faces: 6 (all squares)
- Edges: 12

Same as rectangular prism — just all sides equal.

✔ 8 - 12 + 6 = 2 ✔️

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Shape 7: Sphere

- Name: Sphere
- Vertices: 0
- Faces: 0? Or 1?
Again — in elementary math, sphere is considered to have:
→ 0 vertices, 0 faces, 0 edges — because it’s completely curved with no flat parts.

Some might say 1 face (the whole surface), but typically in these worksheets, sphere has 0 faces, 0 edges, 0 vertices.

Let’s confirm: Yes — standard answer for K-8:
Sphere: 0 vertices, 0 faces, 0 edges

Because “faces” are flat surfaces, and sphere has none.

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Shape 8: Octahedron? Wait — looks like two pyramids stuck together at base — that’s an octahedron? Actually, it’s a square bipyramid — which is an octahedron.

But let’s count:

It has:
- 6 vertices? Let’s see: top point, bottom point, and 4 around middle? No — actually, this shape is called a square bipyramid, and it has:
→ 6 vertices? Wait — no.

Actually, looking at the drawing: it’s two square pyramids glued at their bases — so total vertices: 4 (around the middle) + 1 top + 1 bottom = 6 vertices.

Faces: 8 triangular faces (4 on top, 4 on bottom)

Edges: Each pyramid has 8 edges? No — when glued, the base edges are internal.

Better way:
Total edges: 12? Let’s think.

Each pyramid has 8 edges? No — a square pyramid has 8 edges? Earlier we said 8 for square pyramid? Wait no — earlier for shape 4 (square pyramid) we said 8 edges? That was wrong!

Mistake here!

Let’s correct:

For a square pyramid:
- Base: 4 edges
- From each base corner to apex: 4 edges
→ Total edges: 8? But that can’t be — because Euler’s formula: V=5, F=5, then E should be 8? 5 - 8 + 5 = 2 — yes, it works.

But actually, standard square pyramid has 8 edges? Let me visualize:

Base: 4 edges.

Then 4 edges going up to apex.

Total 8 edges. Yes.

Now for shape 8: it’s two square pyramids glued at their bases.

So:
- Vertices: 4 (base corners) + 1 top apex + 1 bottom apex = 6 vertices
- Faces: 4 (top triangles) + 4 (bottom triangles) = 8 faces
- Edges: The base edges are now internal — so we don’t count them twice. Original each pyramid had 8 edges, but the 4 base edges are shared and become internal — so total edges = 8 + 8 - 4 = 12? Or better: the outer edges are: 4 from top apex to base, 4 from bottom apex to base, and the 4 base edges are still there? No — when you glue, the base is inside, so those 4 edges are not on the surface.

Actually, in the resulting solid, the edges are:
- 4 edges from top apex to the 4 base vertices
- 4 edges from bottom apex to the 4 base vertices
- And the 4 base edges are still present? No — when you glue two pyramids at the base, the base becomes internal, so those 4 edges are no longer on the surface. So only the lateral edges remain.

Wait — no, the base edges are still part of the surface? I'm getting confused.

Let me look for standard name: This shape is called a regular octahedron if all faces are equilateral triangles. A regular octahedron has:
- 6 vertices
- 8 faces
- 12 edges

Yes! And Euler: 6 - 12 + 8 = 2 ✔️

So for shape 8:
Name: Octahedron (or square bipyramid)
Vertices: 6
Faces: 8
Edges: 12

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Shape 9: Pentagonal Prism? Looks like a prism with pentagon base.

Count:
- Two pentagonal bases → 5 vertices each → 10 vertices? But wait, in the drawing, it might be truncated or something? No, it looks like a pentagonal prism.

Actually, looking closely: it has a pentagon on front and back, connected by rectangles.

So:
- Vertices: 10 (5 on front, 5 on back)
- Faces: 7 (2 pentagons + 5 rectangles)
- Edges: 15 (5 on front, 5 on back, 5 connecting them)

✔ Check: 10 - 15 + 7 = 2 ✔️

Name: Pentagonal prism

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Now Extension Part:

Shapes A, B, C are types of prisms or pyramids.

Given:

A) Vertices: ?, Faces: 12, Edges: 18

Use Euler’s formula: V - E + F = 2

So V - 18 + 12 = 2 → V - 6 = 2 → V = 8

What shape has 8 vertices, 12 faces, 18 edges?

That sounds like a hexagonal prism? Let’s check:

Hexagonal prism:
- Vertices: 12? No — hexagon has 6 vertices per base → 12 vertices total.

Wait — 8 vertices? That doesn’t match.

Perhaps it’s a different shape.

List known shapes:

Cube: 8V, 6F, 12E — not matching.

Octahedron: 6V, 8F, 12E — no.

What has 12 faces? Dodecahedron has 12 faces, but that’s 20 vertices, 30 edges.

Not matching.

Perhaps it’s a prism.

General prism: if base has n sides, then:
- Vertices: 2n
- Faces: n + 2 (n rectangles + 2 bases)
- Edges: 3n

Set faces = 12: n + 2 = 12 → n = 10 → decagonal prism

Then vertices = 2*10 = 20, edges = 3*10 = 30 — not matching given edges 18.

Set edges = 18: 3n = 18 → n = 6 → hexagonal prism

Then faces = 6 + 2 = 8, vertices = 12 — not matching given faces 12.

Conflict.

Perhaps it’s a pyramid.

Pyramid: base n-gon
- Vertices: n+1
- Faces: n+1 (n triangles + 1 base)
- Edges: 2n

Set faces = 12: n+1 = 12 → n=11 → hendecagonal pyramid

Vertices = 12, edges = 22 — not 18.

Not matching.

Another idea: perhaps it’s a bipyramid or other.

Use Euler: V - E + F = 2

Given F=12, E=18, so V = 2 + E - F = 2 + 18 - 12 = 8

So V=8, F=12, E=18

What shape is that?

I recall that a cuboctahedron has 12 vertices, 14 faces, 24 edges — no.

Perhaps it’s a truncated tetrahedron or something — too advanced.

Wait — maybe it’s a hexagonal bipyramid?

Hexagonal bipyramid: two hexagonal pyramids glued at base.

Vertices: 6 (base) + 2 apices = 8 vertices

Faces: 12 triangles (6 on each pyramid)

Edges: each pyramid has 12 edges? Hexagonal pyramid: base 6 edges, 6 lateral edges → 12 edges per pyramid, but when glued, the 6 base edges are internal, so total edges = 12 + 12 - 6 = 18? Or the lateral edges are 6+6=12, and the base edges are gone, so only 12 edges? No.

Standard hexagonal bipyramid:
- Vertices: 8 (6 equatorial + 2 polar)
- Faces: 12 (all triangles)
- Edges: 18 (6 from top to equator, 6 from bottom to equator, and 6 around equator? But when glued, the equator edges are shared.

Actually, in a bipyramid, the equator is not an edge — the faces are triangles meeting at the equator.

Number of edges: each of the 12 faces has 3 edges, but each edge shared by 2 faces, so total edges = (12*3)/2 = 18

Vertices: 8

Faces: 12

Perfect!

And Euler: 8 - 18 + 12 = 2 ✔️

So shape A is a hexagonal bipyramid or simply bipyramid with hexagonal base.

But in elementary terms, they might call it a type of pyramid or just give the counts.

The question says "Shapes A and B are types of prisms and shape C is a type of pyramid."

But hexagonal bipyramid is not a prism — it's a bipyramid.

Perhaps I misidentified.

Another possibility: a prismatoid or other.

Let's list the given for extension:

A) ? , V=?, F=12, E=18 → we got V=8

B) ? , V=?, F=16, E=24 → V = 2 + 24 - 16 = 10

C) ? , V=?, F=6, E=10 → V = 2 + 10 - 6 = 6

And it says A and B are prisms, C is pyramid.

For a prism: if base has n sides, then:
V = 2n
F = n + 2
E = 3n

For A: F=12 = n+2 → n=10, then V=20, E=30 — but given E=18, not match.

Unless it's not a right prism or something.

Perhaps "prism" here includes other types, but unlikely.

Another thought: perhaps for A, it's a different interpretation.

Let's calculate what n would be for prism with E=18: 3n=18 → n=6, then F=8, V=12 — but given F=12, not match.

For B: E=24, 3n=24 → n=8, F=10, V=16 — but given F=16, not match.

For C: pyramid, E=10, for pyramid E=2n, so 2n=10 → n=5, then V=n+1=6, F=n+1=6 — oh! Matches C: V=6, F=6, E=10

Yes! For a pentagonal pyramid:
- Base: 5 sides
- Vertices: 5 + 1 = 6
- Faces: 5 triangles + 1 pentagon = 6
- Edges: 5 (base) + 5 (lateral) = 10

Perfect.

So C is pentagonal pyramid

Now for A and B, if they are prisms, but the numbers don't match standard prisms.

Perhaps "prism" is used loosely, or perhaps it's a different shape.

For A: V=8, F=12, E=18

What if it's a cube with something, but no.

Another idea: perhaps it's a truncated pyramid or frustum, but complicated.

Let's think of Archimedean solids, but too advanced.

Perhaps for this level, they expect us to use Euler's formula and not worry about the name, but the task asks for name.

Looking back at the worksheet, for extension, it says "Work out what shapes they are." and gives the properties.

For A: with V=8, F=12, E=18, and it's supposed to be a prism.

But no prism has those numbers.

Unless it's a prism with non-polygonal base, but unlikely.

Perhaps I miscalculated Euler.

V - E + F = 2

For A: V - 18 + 12 = 2 → V = 8, correct.

Now, is there a prism with 8 vertices? That would be a quadrilateral prism, i.e., rectangular prism or cube, which has 6 faces, not 12.

No.

Another possibility: "prism" might include antiprisms or other, but antiprism for n=4: square antiprism has 8 vertices, 10 faces, 16 edges — not matching.

For n=5: pentagonal antiprism: 10 vertices, 12 faces, 20 edges — close but not.

10V, 12F, 20E — but we have 8V, 12F, 18E.

Not matching.

Perhaps it's a different type.

Let's consider that for A, it might be a hexagonal prism but with additional cuts, but no.

Another thought: in some contexts, a "prism" could mean something else, but I think there's a mistake.

Let's look at B: V=10, F=16, E=24

Euler: 10 - 24 + 16 = 2, good.

If it's a prism, 3n=24 → n=8, then F=10, V=16 — but given F=16, V=10, so not.

If it's a pyramid, 2n=24 → n=12, V=13, F=13 — not.

What shape has 10 vertices, 16 faces, 24 edges?

For example, a pentagonal bipyramid has 7 vertices, 10 faces, 15 edges — no.

A gyroelongated square bipyramid or something — too complex.

Perhaps for this level, they intend for us to recognize that for a prism, the number of faces is n+2, etc., but it doesn't fit.

Let's read the instruction: "Shapes A and B are types of prisms and shape C is a type of pyramid."

For C, we have it: pentagonal pyramid.

For A and B, perhaps they are not regular prisms, or perhaps I need to find n such that the formulas work, but they don't.

Another idea: perhaps "prism" here means a prism-like shape, but let's calculate the number of sides.

For a prism, the number of edges is 3n, faces n+2, vertices 2n.

For A: if F=12 = n+2, then n=10, but then E should be 30, but given 18, so not.

Unless the formula is different.

Perhaps for A, it's a pyramid, but the instruction says A and B are prisms.

Let's check the numbers again.

For A: F=12, E=18, V=8

Notice that 12 faces, 18 edges, 8 vertices.

This matches the cuboctahedron? Cuboctahedron has 12 vertices, 14 faces, 24 edges — no.

I recall that a rhombic dodecahedron has 14 vertices, 12 faces, 24 edges — no.

Perhaps it's a truncated octahedron — 24 vertices, 14 faces, 36 edges — no.

Let's search for polyhedron with 8 vertices, 12 faces, 18 edges.

Upon thinking, this is the hexagonal bipyramid as I said earlier, which is not a prism.

But the worksheet says "types of prisms", so perhaps there's a mistake in my assumption.

Another possibility: perhaps "prism" includes the case where the base is not convex or something, but unlikely.

Let's look at B: V=10, F=16, E=24

This could be a pentagonal prism with additional features, but standard pentagonal prism has V=10, F=7, E=15 — not.

If it's a bipyramid: for example, octagonal bipyramid: V=10 (8+2), F=16, E=24 — yes!

Octagonal bipyramid:
- Vertices: 8 (equator) + 2 (poles) = 10
- Faces: 16 triangles (8 on each side)
- Edges: each face has 3 edges, total 16*3/2 = 24 edges

Perfect.

And for A: hexagonal bipyramid: V=8, F=12, E=18

But the worksheet says "prisms", not bipyramids.

Perhaps in this context, "prism" is a misnomer, or perhaps for C it's pyramid, and A and B are also pyramids or something.

The instruction says: "Shapes A and B are types of prisms and shape C is a type of pyramid."

But bipyramids are not prisms.

Unless they consider bipyramids as a type of prism, which they're not.

Perhaps for A, it's a different shape.

Let's consider that for a prism, if it's a right prism, but still.

Another idea: perhaps "prism" here means a prism with polygonal base, but the numbers don't match, so maybe it's a trick, and we should use the properties to find the name based on common shapes.

For C, we have pentagonal pyramid.

For A: with 8 vertices, 12 faces, 18 edges, and it's called a prism, but no standard prism fits.

Perhaps it's a cube with pyramids on faces or something, but complicated.

Let's calculate the average or something.

Perhaps for this level, they expect us to say for A: since F=12, and for a prism F=n+2, so n=10, but then E should be 30, but it's 18, so not.

I think there might be a mistake in the worksheet or in my reasoning.

Let's double-check the extension part.

The user wrote:

"Extension
Shapes A and B are types of prisms and shape C is a type of pyramid.
Work out what shapes they are.

A) Name: ? , Vertices: ? , Faces: 12 , Edges: 18

B) Name: ? , Vertices: ? , Faces: 16 , Edges: 24

C) Name: ? , Vertices: ? , Faces: 6 , Edges: 10"

And for C, as above, pentagonal pyramid: V=6, F=6, E=10 — perfect.

For A: if it were a prism, but it's not matching, perhaps it's a pyramid.

If A is a pyramid, then F = n+1 = 12 → n=11, V=12, E=22 — not 8 and 18.

Not.

Another possibility: perhaps "prism" includes the case of a prism with star base or something, but unlikely.

Let's use the fact that for a prism, the number of edges is 3 times the number of sides of the base, etc.

Perhaps for A, it's a hexagonal prism, but with F=8, not 12.

I recall that a truncated tetrahedron has 12 vertices, 8 faces, 18 edges — close but not.

12V, 8F, 18E — but we have 8V, 12F, 18E.

So swapped.

In fact, the dual of truncated tetrahedron is triakis tetrahedron, which has 8 vertices, 12 faces, 18 edges — yes!

Triakis tetrahedron is a Catalan solid, with 8 vertices, 12 faces (isosceles triangles), 18 edges.

But is it a prism? No.

And for elementary level, probably not.

Perhaps for this worksheet, they intend for us to use Euler's formula and not worry about the name, but the task asks for name.

Let's look at B: V=10, F=16, E=24

This could be a pentagonal bipyramid but that has 7 vertices.

Or octagonal bipyramid as I said: 10 vertices, 16 faces, 24 edges.

Similarly for A: hexagonal bipyramid: 8 vertices, 12 faces, 18 edges.

And for C: pentagonal pyramid: 6 vertices, 6 faces, 10 edges.

Now, the worksheet says "A and B are types of prisms" — but bipyramids are not prisms. However, perhaps in some contexts, or perhaps it's a mistake, and they mean "polyhedrons" or something.

Maybe "prism" is used for bipyramid in some regions, but I doubt it.

Another idea: perhaps for A, it's a prism with a different definition.

Let's calculate the number of sides.

For a prism, the number of faces is always even if the base is polygon, but 12 is even.

Perhaps it's a prism with n=6, but then F=8.

I think I have to go with the bipyramid interpretation, as it fits perfectly.

Perhaps the worksheet has a typo, and for A, faces are 8, but it's written 12.

But in the user's message, it's "Faces: 12" for A.

Let's assume that for this level, they want us to identify based on the counts, and for A and B, they are bipyramids, even though the instruction says "prisms".

Perhaps "prism" is a red herring, or perhaps in the context, "prism" means something else.

Let's read the instruction again: "Shapes A and B are types of prisms and shape C is a type of pyramid."

But for C, it's clearly a pyramid.

For A and B, if they are prisms, then for a prism, the number of vertices is even, which it is for A (8) and B (10), but the face count doesn't match.

Unless it's not a right prism, but still, the topology is the same.

I think I found a possibility: perhaps "prism" here includes the case of a prism with the base being a polygon, but for A, if it's a hexagonal prism, F=8, but given 12, so not.

Another thought: perhaps for A, it's a cube with each face divided, but no.

Let's consider that the shape might be a rhombicuboctahedron or other, but too many vertices.

Perhaps for this worksheet, they expect for A: since F=12, and for a prism F=n+2, so n=10, and ignore the edge count, but that would be inaccurate.

I recall that in some systems, a "prism" can have lateral faces that are not rectangles, but still, the count should be the same.

Let's calculate what n should be for the edge count.

For a prism, E = 3n

For A, E=18, so n=6, then F=8, V=12 — but given F=12, V=8, so not.

For B, E=24, n=8, F=10, V=16 — given F=16, V=10, so not.

Notice that for A, V=8, F=12, E=18, and 8+12-18=2, good.

For B, 10+16-24=2, good.

For C, 6+6-10=2, good.

Now, for a pyramid, as in C, it works with n=5.

For a bipyramid, as I said, for a n-gonal bipyramid:
- Vertices: n + 2
- Faces: 2n
- Edges: 3n

For A: if 2n = 12, then n=6, V=6+2=8, E=3*6=18 — perfect! So hexagonal bipyramid.

For B: 2n = 16, n=8, V=8+2=10, E=3*8=24 — perfect! Octagonal bipyramid.

For C: pyramid, n=5, V=6, F=6, E=10 — pentagonal pyramid.

So even though the worksheet says "prisms" for A and B, it must be a mistake, and they mean "bipyramids" or "double pyramids".

Perhaps in some curricula, bipyramids are classified under prisms, but I doubt it.

Given that, I'll go with that.

So for extension:

A) Name: Hexagonal bipyramid (or hexagonal dipyramid)
Vertices: 8
Faces: 12
Edges: 18

B) Name: Octagonal bipyramid
Vertices: 10
Faces: 16
Edges: 24

C) Name: Pentagonal pyramid
Vertices: 6
Faces: 6
Edges: 10

And for the main part, we have the answers.

Now to summarize all.

First, let's list the main shapes with correct names and counts.

Shape 1: Rectangular prism
- Vertices: 8
- Faces: 6
- Edges: 12

Shape 2: Triangular prism
- Vertices: 6
- Faces: 5
- Edges: 9

Shape 3: Cone
- Vertices: 1
- Faces: 2 (base and curved surface)
- Edges: 1 (circular edge) — but as discussed, some say 0, but for this level, likely 1. However, upon second thought, in many standardized tests, cone has 0 edges because edges are straight. Let me confirm with a reliable source.

Upon recalling, in Common Core standards for grade 1-2, they teach that a cone has 1 face (curved), 1 vertex, and 0 edges. But in grade 3-5, they might say 2 faces.

To resolve, let's look at the worksheet itself. In shape 3, it's a cone, and typically in such worksheets, they expect:
- Vertices: 1
- Faces: 2 (if they count the base)
- Edges: 1 or 0

But in the answer key for similar worksheets, often:
Cone: 1 vertex, 2 faces, 1 edge

For example, on Math-Aids.com or other sites.

I think for consistency, we'll use:
Cone: 1 vertex, 2 faces, 1 edge

Similarly for cylinder.

Shape 4: Square pyramid
- Vertices: 5
- Faces: 5
- Edges: 8

Shape 5: Cylinder
- Vertices: 0
- Faces: 2 (two circular bases)
- Edges: 0 (since no straight edges)

Shape 6: Cube
- Vertices: 8
- Faces: 6
- Edges: 12

Shape 7: Sphere
- Vertices: 0
- Faces: 0
- Edges: 0

Shape 8: Octahedron (or square bipyramid)
- Vertices: 6
- Faces: 8
- Edges: 12

Shape 9: Pentagonal prism
- Vertices: 10
- Faces: 7
- Edges: 15

For shape 8, is it octahedron or square bipyramid? Same thing for regular case.

Now for extension, as above.

So let's write the final answers.

First, for the main part:

1) Name: Rectangular prism
Vertices: 8
Faces: 6
Edges: 12

2) Name: Triangular prism
Vertices: 6
Faces: 5
Edges: 9

3) Name: Cone
Vertices: 1
Faces: 2
Edges: 1

4) Name: Square pyramid
Vertices: 5
Faces: 5
Edges: 8

5) Name: Cylinder
Vertices: 0
Faces: 2
Edges: 0

6) Name: Cube
Vertices: 8
Faces: 6
Edges: 12

7) Name: Sphere
Vertices: 0
Faces: 0
Edges: 0

8) Name: Octahedron
Vertices: 6
Faces: 8
Edges: 12

9) Name: Pentagonal prism
Vertices: 10
Faces: 7
Edges: 15

Extension:

A) Name: Hexagonal bipyramid
Vertices: 8
Faces: 12
Edges: 18

B) Name: Octagonal bipyramid
Vertices: 10
Faces: 16
Edges: 24

C) Name: Pentagonal pyramid
Vertices: 6
Faces: 6
Edges: 10

Note: For A and B, although the worksheet says "prisms", the properties match bipyramids, so we use that. If your teacher expects something else, adjust accordingly, but mathematically, this is correct.

Now for the final answer, since the user asked to solve the problem, I'll provide the filled-in values.

But the response format requires Final Answer section with only the final correct answer, but since it's multiple parts, I'll list them.

Perhaps box the entire thing, but that's messy.

Since the instruction is to provide the final answer after reasoning, and for this type, it's a set of answers, I'll write them clearly.

Final Answer:

For the main shapes:

1) Name: Rectangular prism, Vertices: 8, Faces: 6, Edges: 12
2) Name: Triangular prism, Vertices: 6, Faces: 5, Edges: 9
3) Name: Cone, Vertices: 1, Faces: 2, Edges: 1
4) Name: Square pyramid, Vertices: 5, Faces: 5, Edges: 8
5) Name: Cylinder, Vertices: 0, Faces: 2, Edges: 0
6) Name: Cube, Vertices: 8, Faces: 6, Edges: 12
7) Name: Sphere, Vertices: 0, Faces: 0, Edges: 0
8) Name: Octahedron, Vertices: 6, Faces: 8, Edges: 12
9) Name: Pentagonal prism, Vertices: 10, Faces: 7, Edges: 15

Extension:
A) Name: Hexagonal bipyramid, Vertices: 8, Faces: 12, Edges: 18
B) Name: Octagonal bipyramid, Vertices: 10, Faces: 16, Edges: 24
C) Name: Pentagonal pyramid, Vertices: 6, Faces: 6, Edges: 10

Note: For cone and cylinder, some curricula may define faces and edges differently; if your class uses different definitions, adjust accordingly. For example, some say cone has 1 face and 0 edges, cylinder has 2 faces and 0 edges, etc. But the above is commonly accepted in elementary math.