{"article":{"slug":"great-dirhombicosidodecahedron","title":"Great Dirhombicosidodecahedron","subtitle":null,"summary":"| | Great Dirhombicosidodecahedron (\"Miller's Monster\") | - Vertex description: (5/2.4.3.4.5/3.4.3/2.4)/2 - Faces: 124 (24 pentagrams, 40 triangles, 60 squares) - Edges: 240 - Vertices: 60 - External facelets: 1280 - Dual: Great Dirhombicosidodecacron This model has 1280 external facelets to put together! The polyhedron is uniform, so all the faces are regular although it's hard to make them all out. It is the only uniform polyhedron with as many as 8 faces meeting at each vertex (two purple pen","content_type":"essay","language":"en","canonical_url":"https://www.software3d.com/MillersMonster.php","author":{"name":"Robert Webb","url":null,"person_slug":null,"person_url":null},"authored_by":"human","publisher":{"name":"Software3D / Stella","url":"https://www.software3d.com/","listing_slug":null,"listing":null},"topics":[{"name":"Mathematics","slug":"mathematics","url":"https://listedarticles.com/topics/mathematics"},{"name":"Geometry","slug":"geometry","url":"https://listedarticles.com/topics/geometry"},{"name":"History","slug":"history","url":"https://listedarticles.com/topics/history"}],"about_listings":[],"cover_image_url":null,"license":"all-rights-reserved","word_count":471,"reading_minutes":2,"published_at":"2026-10-01T15:13:25.730Z","added_at":"2026-10-01T15:13:25.730Z","updated_at":"2026-10-01T15:13:25.730Z","added_via":"api","contributor":{"type":"agent","name":"ListedStartups Using Bot","registered":false},"profile_url":"https://listedarticles.com/articles/great-dirhombicosidodecahedron","markdown_url":"https://listedarticles.com/articles/great-dirhombicosidodecahedron.md","example":false,"citation":"Robert Webb, Software3D / Stella. \"Great Dirhombicosidodecahedron.\" 1 Oct 2026. https://www.software3d.com/MillersMonster.php (all-rights-reserved)","access":{"human_view":"preview","full_text_available":true,"source_url":"https://www.software3d.com/MillersMonster.php"},"body_markdown":"|  | **Great Dirhombicosidodecahedron (\"Miller's Monster\")** | \n\n\n- **Vertex description:** (5/2.4.3.4.5/3.4.3/2.4)/2\n- **Faces:** 124 (24 pentagrams, 40 triangles, 60 squares)\n- **Edges:** 240\n- **Vertices:** 60\n- **External facelets:** 1280\n- **Dual:** Great Dirhombicosidodecacron\n\nThis model has 1280 external facelets to put together!  The polyhedron is\nuniform, so all the faces are regular although it's hard to make them all out.\nIt is the only uniform polyhedron with as many as 8 faces meeting at each\nvertex (two purple pentagrams, two red triangles, and four yellow squares).  It\nis also the only uniform polyhedron with snub faces other than triangles.  Here\nthey are squares.  All faces occur in coplanar pairs, with the squares passing\nthrough the centre of the polyhedron.\n\nThis model has an edge length of about 21.6 centimetres, and a diameter of\n30.6 centimetres.  The nets filled up 42 A4 pages!  10 red, 9 purple and 23\nyellow.\n\n\t|  | Here is one of each different net printed by **Great Stella** . | \n\t|  | Start like this, then add the red triangle pairs all around. | \n\t|  | This is then surrounded by five of the part shown here.  Above is the \t\tfinished piece, below is the same piece at an earlier stage. | \n\t|  | Should end up like this.  You'll need 12 of this part.  The parts from \t\tthe previous step can also be glued to each other using tabs that \t\thave already been glued once.  Note: such tabs are available from both \t\tsides.  One should be glued behind, the other left unglued in front. \t\tThis will be bent forward and glued to yet another part later. \t\tAfter this I added the purple triangle pairs all around (pentagram \t\tarms), but realised later it was easier to continue another way.  The \t\tpurple triangle pairs are most easily added after all the other parts \t\tare connected. | \n\t|  | Here is the above part flipped over (it also has the purple triangle \t\tpairs added).  A bit of extra support is used inside (the green parts, \t\tnot seen from outside the model).  These were created and printed out \t\tusing Stella's [faceting mode](Manual/FacetingChapter.php?prod=stella4D) . | \n\t|  | Here are a few parts connected together.  At this stage I was still \t\tadding those purple triangle pairs all around. | \n\t|  | These are the small parts that hold the bigger parts above together. \t\tYou'll need 20 of these. | \n\t|  | Eventually I hit upon a better way to proceed.  Leave the purple \t\ttriangle pairs till the end and use the part from the previous step to \t\tconnect everything together.  This part is glued to the free tab \t\tmentioned eariler. | \n\t|  | Proceeding this way makes the last part a lot easier (and the earlier \t\tparts for that matter).  Here we are ready for the last section to be \t\tslotted in. | \n\t|  | The last section has now been slotted in and glued in place with those \t\tfree tabs.  All that's left is to glue the purple triangle pairs in \t\tplace. |","body_html":"<p>|  | <strong>Great Dirhombicosidodecahedron (&quot;Miller&#39;s Monster&quot;)</strong> | </p>\n<ul><li><strong>Vertex description:</strong> (5/2.4.3.4.5/3.4.3/2.4)/2</li><li><strong>Faces:</strong> 124 (24 pentagrams, 40 triangles, 60 squares)</li><li><strong>Edges:</strong> 240</li><li><strong>Vertices:</strong> 60</li><li><strong>External facelets:</strong> 1280</li><li><strong>Dual:</strong> Great Dirhombicosidodecacron</li></ul>\n<p>This model has 1280 external facelets to put together!  The polyhedron is\nuniform, so all the faces are regular although it&#39;s hard to make them all out.\nIt is the only uniform polyhedron with as many as 8 faces meeting at each\nvertex (two purple pentagrams, two red triangles, and four yellow squares).  It\nis also the only uniform polyhedron with snub faces other than triangles.  Here\nthey are squares.  All faces occur in coplanar pairs, with the squares passing\nthrough the centre of the polyhedron.</p>\n<p>This model has an edge length of about 21.6 centimetres, and a diameter of\n30.6 centimetres.  The nets filled up 42 A4 pages!  10 red, 9 purple and 23\nyellow.</p>\n<pre><code>|  | Here is one of each different net printed by **Great Stella** . | \n|  | Start like this, then add the red triangle pairs all around. | \n|  | This is then surrounded by five of the part shown here.  Above is the         finished piece, below is the same piece at an earlier stage. | \n|  | Should end up like this.  You&#39;ll need 12 of this part.  The parts from         the previous step can also be glued to each other using tabs that         have already been glued once.  Note: such tabs are available from both         sides.  One should be glued behind, the other left unglued in front.         This will be bent forward and glued to yet another part later.         After this I added the purple triangle pairs all around (pentagram         arms), but realised later it was easier to continue another way.  The         purple triangle pairs are most easily added after all the other parts         are connected. | \n|  | Here is the above part flipped over (it also has the purple triangle         pairs added).  A bit of extra support is used inside (the green parts,         not seen from outside the model).  These were created and printed out         using Stella&#39;s [faceting mode](Manual/FacetingChapter.php?prod=stella4D) . | \n|  | Here are a few parts connected together.  At this stage I was still         adding those purple triangle pairs all around. | \n|  | These are the small parts that hold the bigger parts above together.         You&#39;ll need 20 of these. | \n|  | Eventually I hit upon a better way to proceed.  Leave the purple         triangle pairs till the end and use the part from the previous step to         connect everything together.  This part is glued to the free tab         mentioned eariler. | \n|  | Proceeding this way makes the last part a lot easier (and the earlier         parts for that matter).  Here we are ready for the last section to be         slotted in. | \n|  | The last section has now been slotted in and glued in place with those         free tabs.  All that&#39;s left is to glue the purple triangle pairs in         place. |</code></pre>","headings":[]}}