Timelapse are good to learn only if you’re experimented with Blender, if you’re not experimented they’re near useless if you look for tutorials.
And this timelapse is for an older version of Blender that has a very different interface in comparison to the current version.
Here’s what is done in the video adapted to the latest release of Blender :
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Be in Object Mode, go in Front view ( View -> Front or press Numpad 1 )
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On the Blender top header click on Add -> Mesh -> Icosphere
It will add an icosphere at the 3D Cursor location
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Click somewhere to the right of the icosphere to move the 3D Cursor there, then click SHIFT+S and select “Cursor to Grid” (or click Object -> Snap -> Cursor to Grid)
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again on the Blender top header click on Add -> Mesh -> Cone
note : by default in latest Blender the bottom of the cone is an ngon, if you want/need to make that base into tris, just after adding it press F6 (or look in the operator tab, at the bottom of the toolshelf, in the left of the 3D view) and change “Base fill type” from “ngon” to “triangle fan”.
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important note : the orange dot in the center is the “Origin” of the cone, this is important to know because it’s the origin that will be used for where the cone will be duplivert-ed on the icosphere
You can move the Origin point to anywhere by moving the 3D cursor at a location and in Object Mode click on the button Origin -> Origin to 3D Cursor.
But for this we will not be moving it
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Press S (to scale) and resize the cone in Object Mode (we could do in Edit Mode too, but i do it there so i can mention applying scale and rotation after 
because it’s something you must know)
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Press CTRL+A -> Rotation&Scale (or Object -> Apply -> Rotation&Scale) to avoid problem that happen for further operations if we rescale/rotate in object mode and do not apply those.
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Go to Edit Mode, select the pointy top and move it a bit (after selecting it , press G and press Z to constraint it to the Z axis so we move it up very easily)
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Go back to Object Mode
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Select the cone (it should be already selected anyways) , hold the SHIFT key then select the icosphere
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Press CTRL+P and select “Object” (or click Object -> Parent -> Object then confirm Object) , it will create a line between the cone and the icosphere.
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Now select the Icosphere only
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To the right of the view, click on the Object panel
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Look/scroll down until you see the “Duplication tab”
Click on the “Verts” to activate the Dupliverts function.
Then enable the “Rotation” button
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Look into the 3D View :
-It’s actually good even if it seems odd for now 
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Select the original cone in the middle of the duplicated ones.
Under the “Duplication” tab there is a “Relation Extra” tab, notice that Axis by default is set to +Y
Change it to +Z instead
resulting in :
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Now select the icosphere, press SHIFT + S and select “Cursor to Selected”
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Select the original cone (don’t worry, even if it’s hidden by the duplicate, they’re not real so you can’t select them if you click on them, it will select the only real object under your click, the original cone) and press SHIFT + S then select “Selection to Cursor”
result :
Note : the dupliverts are still not real, you can’t select 1 and delete it yet.
To do so, you’ll need to make them real first.
Select the icosphere, click Object -> Apply -> Make Duplicate Real
That’s it, each cone is now a real object that you can edit/remove as you wish
And you can remove the original cone that is now inside of the icosphere
(you can select the icosphere, press H to hide it from view, select the central cone and delete it, the press ALT+H to un-hide the central cone)
(you can use the Outliner , and directly select the original cone from there)
