---
title: "Great Dirhombicosidodecahedron"
slug: great-dirhombicosidodecahedron
url: https://listedarticles.com/articles/great-dirhombicosidodecahedron
canonical_url: https://www.software3d.com/MillersMonster.php
content_type: essay
language: en
published_at: 2026-10-01T15:13:25.730Z
updated_at: 2026-10-01T15:13:25.730Z
author: "Robert Webb"
authored_by: human
publisher: "Software3D / Stella"
publisher_url: https://www.software3d.com/
topics: ["Mathematics", "Geometry", "History"]
license: all-rights-reserved
word_count: 471
reading_minutes: 2
citation: "Robert Webb, Software3D / Stella. \"Great Dirhombicosidodecahedron.\" 1 Oct 2026. https://www.software3d.com/MillersMonster.php (all-rights-reserved)"
# The full text follows. The web page shows an extract and sends readers
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---

# Great Dirhombicosidodecahedron

> | | 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

|  | **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 pentagrams, two red triangles, and four yellow squares).  It
is also the only uniform polyhedron with snub faces other than triangles.  Here
they are squares.  All faces occur in coplanar pairs, with the squares passing
through the centre of the polyhedron.

This model has an edge length of about 21.6 centimetres, and a diameter of
30.6 centimetres.  The nets filled up 42 A4 pages!  10 red, 9 purple and 23
yellow.

	|  | Here is one of each different net printed by **Great Stella** . | 
	|  | Start like this, then add the red triangle pairs all around. | 
	|  | 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. | 
	|  | Should end up like this.  You'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. | 
	|  | 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's [faceting mode](Manual/FacetingChapter.php?prod=stella4D) . | 
	|  | Here are a few parts connected together.  At this stage I was still 		adding those purple triangle pairs all around. | 
	|  | These are the small parts that hold the bigger parts above together. 		You'll need 20 of these. | 
	|  | 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. | 
	|  | 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. | 
	|  | The last section has now been slotted in and glued in place with those 		free tabs.  All that's left is to glue the purple triangle pairs in 		place. |