This 120 faces polyhedron hides several outstanding properties:


Remarks: This 120polyhedron can by built by assembling 30 pyramids on the faces of a rhombic triacontahedron; there are no pyramids in the compound of five octahedra which also has 120=5x(6x4) triangular faces (but no four of the five vertices which define a "peak" are coplanar).
The first stellation of the icosidodecahedron (compound of a regular dodecahedron and a regular icosahedron) is an other 120polyhedron with triangular faces.
starting with a Waterman polyhedron (or with the great rhombicuboctahedron) 
 
Take the Waterman polyhedron with root 7 (48 vertices) and move the hexagonal faces toward the center until the rectangles become squares; now all 26 faces are regular (this Archimedean polyhedron is the great rhombicuboctahedron). Augment each face with an appropriate regular pyramid and you get the first 144polyhedron.  
starting with the cuboctahedron 
 
Take the cuboctahedron with its circumsphere, project the 6+8=14 face's centers on the circumsphere and you get a polyhedron with 26 vertices and 48 identical triangular faces. Augment each face with an irregular tetrahedron (with its apex on the line joining the center of the polygon to the incenter of the face) and you get the second 144polyhedron. 
Remarks:
The two light blue polyhedra (before the final augmentations with pyramids) are dual.
The two 144polyhedra have 144 triangular faces, 74 vertices and 216 edges, but their vertices don't have the same orders (they have different topologies). Both have octahedral symmetry (like the cube).
On the second 144polyhedron the "48 cones of light" described by Lynnclaire can be defined with the center (common apex) and the incircles of the 48 triangles with red sides (bases of the tetrahedra).
references: 
• Lynnclaire Dennis' neardeath experience
• The Pattern by Lynnclaire Dennis, published by Entagram Productions Inc. 1997 an animated gif of "The Pattern" (Robert W. Gray) • the 120polyhedron; the cuboctahedron and CCP approaches of the 144polyhedra by Robert W. Gray 
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convex polyhedra  non convex polyhedra  interesting polyhedra  related subjects  May 2005 updated 25062005 