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I'm using Blender 2.9. I created a wedge, I sliced a box diagonally. I turned on the statistic, I see:

  • 1 object
  • 6 vertices
  • 8 edges
  • 4 faces 8 triangles

But why there are 8 triangles, can someone explain?

enter image description here

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    $\begingroup$ Related blender.stackexchange.com/questions/102597/… as noted in answer below a mesh is tessellated into triangles. A face made up of n verts will be split into (n - 2) triangles. Eg for a a triangular prism (eg a 3 vert cylinder) has (6verts 5 faces 9 edges) with 3 quad faces (3 x (4 - 2)) and two triangle faces (1 x (3 - 2)) = 8 triangles. $\endgroup$
    – batFINGER
    Feb 21 at 4:04
  • $\begingroup$ @susu wouldn't have bothered deleting answer over my query (think it answers the gist of the question) Simply intrigued by the geom count. is it 4 quads all sharing 2 edges? or is it..? $\endgroup$
    – batFINGER
    Feb 21 at 16:57
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    $\begingroup$ The quad faces are naturally split by blender’s internal system. As I understand it, no rendering engine really draws four sided faces. They always draw triangles, then maybe outline “defined” edges. This is why if you bend a four sided face in blender, it comes out as two triangles with a ghost edge across the bent surface. $\endgroup$
    – TheLabCat
    Feb 21 at 17:28
  • $\begingroup$ Any 3D software, under the hood actually only understands faces with 3 sides (tris). This is because for any 3 distinct points in space there will always be a single plane that contains all 3 points, so a tri is always planar. The same cannot be said about 4 points in space, as the fourth point might be offset away from the plane. So every quad is actually made up of two tris "under the hood", even if the edge that splits the quad into two tris is not displayed to the user. The same is true for n-gons, they are always broken up into tris even if you can't see them. $\endgroup$ Aug 17 at 16:47
  • $\begingroup$ Something is wrong, but it's not the tri count. A prism should have 5 faces and 9 edges, yours has 4 faces and 8 edges. Can you show us a wireframe so we can see all edges of the shape? $\endgroup$ Aug 17 at 17:08
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All render engines use triangles.

In blender, each face with 4 vertices is in reality two triangles.

Each of the rectangular faces in the shape you show are comprised of two triangles (see the green lines in the example)

enter image description here

enter image description here

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  • $\begingroup$ am intrigued by the geometry count in question. Appears one edge and one face short of triangular prism, yet has same vert and tri count. $\endgroup$
    – batFINGER
    Feb 21 at 12:47
  • $\begingroup$ @batfinger 2 proper triangles + 6 triangles (in 3 quads) $\endgroup$
    – susu
    Feb 21 at 16:22
  • $\begingroup$ Yes, understand see my comment under question. That's 5 faces count shown in image is 4. $\endgroup$
    – batFINGER
    Feb 21 at 16:35
  • $\begingroup$ @batFINGER There you go $\endgroup$
    – susu
    Feb 21 at 16:40
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Faces are tessellated into triangles.

Due to sense of deja vu re comment on question and since removed answer thought I'd add an answer

All faces are tessellated into triangles on render. The statistics gives us this conversion count using formula outlined here

Finding Vertices, Edges, Faces, and Tris using Python

A face made up of n verts will be split into (n - 2) triangles. Eg for a a triangular prism (eg a 3 vert cylinder) has (6verts 5 faces 9 edges) with 3 quad faces, and two triangles $$(3 \times(4 - 2)) + (2 \times (3 - 2)) = 8$$ triangles

Re question image.

One way to achieve the counts in question image

enter image description here

is to dissolve the edge between quads effectively making an ugly duck 6 vert ngon

>>> for f in C.object.data.polygons:
...     len(f.vertices)
...     
6
3
3
4

which once again

$$4 + 1 + 1 + 2 = 8$$

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  • $\begingroup$ if you dissolve the edge, blender removes everything but one edge and two vertices. How did you manage to accomplish the equivalent? $\endgroup$ Aug 17 at 21:27
  • $\begingroup$ This can be done by dissolving edge but not dissolving vertices in the adjust last operator. $\endgroup$
    – Tiles
    Aug 22 at 7:53
  • $\begingroup$ @MartyFouts missed comment, prob should have elaborated eg dissolve edge between two quads creates a right angle bent 6 vert ngon, 4, 4 -> 6 (or between quad and tri. 4, 3 -> 5) Resultt is an "ugly duck". non-manifold geometry, which tessellates weirdly when transformed in view. For those that cannot see the deleted answer of susu, which FWIW I upvoted, goes over the theory and explains the tri count using a tri prism example. Made a comment re the q geometry, susu chose to remove answer, which IMO was unnecessary, since it's (IMO) the gist of the question. Have attempted to cover both $\endgroup$
    – batFINGER
    Aug 22 at 8:15
  • $\begingroup$ So then you agree with me that it's non-manifold geometry. Do you agree that the original description "sliced a box diagonally" doesn't produce the result? $\endgroup$ Aug 22 at 15:33
  • $\begingroup$ Does it matter? My guess is OP was wondering why 8 tris not 2. Would need to ask OP & ditto for any info re method for object creation. Certainly not worth downvoting any of the answers is it? $\endgroup$
    – batFINGER
    Aug 22 at 16:03
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Any 3D software under the hood actually only 'understands' faces with 3 sides (tris). This is because for any 3 distinct points in space there will always be a single plane that contains all 3 points, so a tri is always planar. The same cannot be said about 4 points in space, as the fourth point might be offset away from the plane. So every quad is actually made up of two tris "under the hood", even if the edge that splits the quad into two tris is not displayed to the user. The same is true for n-gons, they are always broken up into tris even if you can't see them.

So in the stats the tri count includes the tris that make up the quads, each quad is 2 tris.

That's why n-gons are considered bad topology, especially for meshes that will be deformed by an armature: you don't know how the software will split the n-gon into tris and so you don't have as much control over how exactly it will deform, and different softwares might triangulate differently from each other, so if you have to import the mesh to a different software things might not look the same.

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  • $\begingroup$ but that doesn't work in this case, because there are five faces if you do what the OP claimed to have done, and the stats in the question say 4. $\endgroup$ Aug 17 at 21:29
  • $\begingroup$ Well, the question was about the tri count and that's the answer. But you are right, something is wrong in his face and vert count (not the tri count). I asked him in the comments for a wireframe image of his mesh. Something is wrong, but it's not the tri count. He probably has a rogue vertex (when he sliced he might have missed the vertex and created a new one very close to the other), or maybe his geometry is non-manifold. $\endgroup$ Aug 18 at 13:20
  • $\begingroup$ The problem is that given that the other counts are wrong, we can only speculate on what's hidden behind the visible faces, so we can't really say that the tri count is right or wrong. $\endgroup$ Aug 18 at 13:52
  • $\begingroup$ We can say it's right or wrong based on the description. He said he made a "wedge" by slicing a cube diagonally in half. The tri count is what you'd expect from that shape. The vert and edge count on the other hand are not. And there is no 'correct' (manifold, no rogue verts, etc) that can have those counts, it's geometrically impossible. $\endgroup$ Aug 18 at 14:05
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EDIT: My original answer was correct but incomplete. I am adding text to provide a complete answer.

The original question is incomplete and inconsistent. The OP says they "created a wedge [by] slic[ing] a box diagonally." They show what appears to be such a wedge, but they include statistics that don't match a wedge, as there are only 8 edges and 4 faces.

None of us should have answered the question as it stands. It should have been closed for lacking clarity and detail.

The naive answer to the question would be to simply limit the scope of the answer to the described object and the specifics and point out that the described wedge has 3 quad faces, each of which consists of two tries + 2 triangle faces, each of which has 1 trie for a total of 3 * 2 + 2 * 1 = 8 tries. The problem is that the answer ignores two errors in the statistics, if the geometry is in fact a wedge.

The next step would be to explain the existence of the error. This is what I did in my original answer:

Short answer: You have non-manifold geometry.

Create a wedge shape:

wedge shape

You get 6 verts, 9 edges, 5 faces and 8 tris; as I would expect. But your object has fewer edges (8) and fewer faces (4).

I can't actually come up with a manifold geometry that produces the same counts as you have.

There's something about your geometry, that's not obvious from the solid view, that is leading to the count you get.

You can count the edges, faces, and verts on my geometry and they match the counts blender gives. So why do I have 4 faces and 6 tries?

Because when you work with quads or N-gons, blender represents them internally as tris. You can actually see this by selecting all the faces and typing CTRLT:

showing the tries

Of course, when you do this, you make the quads into tries so the numbers all go up. But it does show that each quad is 2 tries, not one, so the tri count for the original should be 3 quads * 2 + 2 tries

  • 1 = 8.

What I wrote was correct, but incomplete. It was incomplete because the third step requires something we should not do in an answer: speculation.

Since the statistics do not match the description or the object implied by the screenshot, what is behind that solid object?

The answer appears to involve creating an 6-gon consisting of all 6 vertices. I've added a Triangulate modifier to such a creature to make it easier to visualize:

6-gone composed of 6 vertices from the original cube

Now if I add the other sides to this I get geometry that matches the original counts:

the creation that satisfies the statistics

and, as you can clearly see from the triangulated version, this creation is non-manifold.

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  • $\begingroup$ That's not a pyramid, it's a prism. But you're right, there should be 9 edges, not 8. Also there should be 5 faces, not 4. $\endgroup$ Aug 17 at 17:05
  • $\begingroup$ fair point. Edited. $\endgroup$ Aug 17 at 21:13
  • $\begingroup$ Downvoter here since the answer does not fit. The problem has nothing to do with non manifold geometry. Batfinger found the solution. The question, to which also i have answered, is already wrong. It's not the tri count that is unexpected here. But the edges count. And this just means that the thread opener must have removed an edge somewhere. $\endgroup$
    – Tiles
    Aug 22 at 7:34
  • $\begingroup$ Batfinger's "solution" is, in fact, non manifold geometry, as he says in his comment to me in his answer. We don't know what's wrong because the solid view is hiding details. You can't "remove an edge somewhere", and end up with manifold geometry. Also, the thread opener claims to have merely cut a cube diagonally, so that means their description of what they did is also wrong. $\endgroup$ Aug 22 at 15:25
  • $\begingroup$ I have to disagree, sorry. A bend quad or n-gon is not non manifold geometry. But the most normal thing in 3D. Even when it goes around an angle of 90 degrees. $\endgroup$
    – Tiles
    Aug 23 at 10:24

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