How to make a Regular Dodecahedron with a 5-pointed star Shape?

Question

How can I make this Regular Dodecahedron shape, with the 5 point star or pentagram? I'm confused with these geometric shapes and settings. How to achieve this? I tried adding it using the Geodesic Dome addon.

Answer 1

That's the shape of a Dodecahedron with a mesh on each face resembling that of a Pentagram. You can easily add this solid in Blender 3.6 via Add > Mesh Function > Regular Solid > Dodecahedron. For other Blender versions, enable the addon Add Mesh: Regular Solids under Edit > Preferences > Add-ons and add it via Add > Mesh > Solids > Platonic > Dodecahedron.

Then tab into Edit Mode and press A to select all faces and press X > Limited Dissolve. With all faces selected go to menu Mesh > Split > Faces by Edges.

Then with all faces still selected press P > By Loose Parts.

This will create separate objects for each face which you can then link later so when you topologize one or any face as Pentagram, it will reflect on each face. But first you have to align each of the 12 face origins to make sure they all face their Face Normals. So first with all objects selected, right click and choose Set Origin > Origin to Geometry.

Now here's the tricky part. Set the Transformation Orientation to View. Then select one object at a time and tab into Edit Mode. Select any Edge and press Shift+NumPad-7 to align the Face Normal to point toward the camera then tab back into Object Mode and go to menu Object > Transform > Align To Transform Orientation. Notice how this aligns the origin to go along the face normal towards the camera. Do this with all 12 faces. You can also easily automate this process as shown in this answer.

Now with all selected objects having aligned origins, press Ctrl+L > Link Object Data. Now you can topologize one face into a Pentagram and it will reflect on all faces as well.

Now tab into any object in Edit Mode and select all vertices and right click then select Subdivide. Select 2 vertices at a time and press J to split the faces into the Pentagram shape. Once you are done, tab back into Object Mode, verify all faces have the same topology reflected and select all objects then press Ctrl+J to join them. Then tab into the merged object and select all vertices with A then press M > Merge By Distance.

Duplicate the object and add a Wireframe Modifier to one object. Then add color materials to the other one.

I'm sure there is an easier way to do this using Geometry Nodes as well.

Answer 2

In my previous Answer I gave a tutorial how to manually model this shape. Here is faster automated way which creates the Dodecahedron and splits it into separate faces that get linked together as same mesh. Just execute this python script in the Text Editor. And then edit any of the object faces. Then select all objects and join with Ctrl+J and merge all vertices in Edit Mode with AM > Merge By Distance. You're done.

import bpy

bpy.ops.mesh.primitive_solid_add(source='12')
bpy.ops.object.mode_set(mode='EDIT')
bpy.ops.mesh.select_all(action='SELECT')
bpy.ops.mesh.dissolve_limited()
bpy.ops.mesh.edge_split(type='EDGE')
bpy.ops.mesh.separate(type='LOOSE')
bpy.ops.object.mode_set(mode='OBJECT')

area_type = 'VIEW_3D'
areas  = [area for area in bpy.context.window.screen.areas if area.type == area_type]
bpy.context.scene.tool_settings.use_transform_data_origin = True
bpy.ops.object.origin_set(type='ORIGIN_GEOMETRY', center='MEDIAN')

selected_objects = bpy.context.selected_objects.copy()
bpy.ops.object.select_all(action='DESELECT')

with bpy.context.temp_override(area=areas[0]):
    for obj in selected_objects:
        bpy.context.view_layer.objects.active = obj
        obj.select_set(True)
        bpy.ops.object.mode_set(mode='EDIT')
        bpy.ops.mesh.select_all(action='SELECT')
        bpy.ops.transform.create_orientation(use=True)
        bpy.ops.object.mode_set(mode='OBJECT')
        transform_type = bpy.context.scene.transform_orientation_slots[0].type
        bpy.ops.transform.transform(mode='ALIGN', orient_type='Face', orient_matrix_type=transform_type, mirror=False, use_proportional_edit=False, proportional_edit_falloff='SMOOTH', use_proportional_connected=False, use_proportional_projected=False, snap=False, snap_elements={'INCREMENT'}, use_snap_project=False, snap_target='ACTIVE', use_snap_self=True, use_snap_edit=True, use_snap_nonedit=True, use_snap_selectable=False)
        bpy.ops.transform.delete_orientation()
        obj.select_set(False)
        
bpy.ops.object.select_all(action='SELECT') 
bpy.ops.object.make_links_data(type='OBDATA')

Answer 3

Another method, using object-instancing:

• Make your Math Function > Regular Solid > Dodecahedron. and X > Limited dissolve its excess edges.
• ShiftD duplicate off one of its faces, and P Separate the selection to a new object.

Now you have to align the pentagon to its own object-origin, as shown on the right.

In Edit Mode:

• Create a Custom Orientation from the single face

In Object Mode ...

• Header > Object > Origin > Origin to Geometry
• Header > 'Options' > Affect Only Origins
• Header > Object > Transform > Align to Transform Orientation
• Option off again, AltG,AltR align the pentagon flat

Back in Edit Mode, annoyingly ..

• RZ -90, so one of the points of your pentagon is down object-Y

• Set the dodecahedron > Object tab > Instancing panel > to 'Faces'
• CtrlP Parent the aligned pentagon to the dodecahedron

.. and any edit to the pentagon (or an AltD instance of it, for convenience) will be reflected in all instances, aligned, ready for CtrlA, Make instances real, CtrlJ Join , and (Edit) M > Merge by Distance.

Answer 4

Warning: Potential Mesh Boolean abuse ⚠️

This post is suspected to have pushed the boolean feature beyond a reasonable extent.

There is reason to believe this technique is not the best approach and has been marked by our community.
Boolean algorithms are esoteric in a sense: the process is so complex behind the scenes, that it's hard to reason about it and predict if it will continue to work in future releases of Blender, or maybe even on different hardware or operating systems (hopefully the calculations aren't architecture-dependent, e.g. 32 vs 64 bit accuracy). Needless to say, trying to repurpose the technique for e.g. a different Rubik's shape may be hell. BTW, did you know "Bool" is pronounced the same as "Ból" in Polish and means "Pain"?

To add salt to injury, I'm using Blender 4.0 αlpha - I tried at first by simply duplicating a custom group multiple times, which worked for me in the past ([1], [2], [3]), but discovered when using Boolean difference, things are not only cut, but also joined! Dealing with it before B3.6 would take a huge amount of nodes. In B3.6 a Simulation Zone could be used, but as you can see I ended up with a nested Repeat Zone, and since you can't nest Simulation Zones, a workaround would again increase the complexity; so if you think the answer is complex enough, hopefully you will forgive me the alpha version usage (I wouldn't dare to ask for forgiving the boolean).

Custom Group (yes, it's within a Repeat Zone and it contains a Repeat Zone):

Result:

I know what you're thinking, but Markus, obviously you just need 10 half-half cuts, aligned to corners:

Yes, as long as you only just want to have the correct outside. The difference can be shown using bevel and animation:

So do you want a dodecahedron equivalent of a 2×2 or 3×3 cube? I interviewed an owner of such Rubik's dodecahedron and he says it only has two types of rotation: one as shown above and the rotation of a single-piece triangular corner:

I don't even have such corner… Yet! An update soon… If Boolean police doesn't get me first.