Triangulated pinched triangular cupola (EntityTopic, 13)

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The triangulated pinched triangular cupola is one of the non-CRF facets of CRF duals currently being studied by Keiji. It is self-dual, however it is not currently marked as such in the polytope explorer as Keiji hasn't yet worked out a permutation that it will accept.[1] It has no symmetry at all (and is therefore chiral), which is the main reason finding such a permutation is a difficult task. The imat is posted twice below, as it has been entered regardless so that it can be used as cells. When a solution is found, these will be replaced with a single imat.

Incidence matrix

Dual: Self-dual

#	TXID	Va	Vb	Vc	Vd	Ve	Vf	Vg	Vh	Ea	Eb	Ec	Ed	Ee	Ef	Eg	Eh	Ei	Ej	Ek	El	Em	En	3a	3b	3c	3d	3e	4a	4b	5a	Type	Name
0	Va																															= point	; white
1	Vb																															= point	; red
2	Vc																															= point	; orange
3	Vd																															= point	; lime
4	Ve																															= point	; green
5	Vf																															= point	; cyan
6	Vg																															= point	; blue
7	Vh																															= point	; pink
8	Ea	1	1	0	0	0	0	0	0																							= digon	; wr !cp
9	Eb	1	0	1	0	0	0	0	0																							= digon	; wo !gc
10	Ec	1	0	0	1	0	0	0	0																							= digon	; wl !lg
11	Ed	1	0	0	0	1	0	0	0																							= digon	; wg !ol
12	Ee	1	0	0	0	0	0	1	0																							= digon	; wb !op
13	Ef	0	1	1	0	0	0	0	0																							= digon	; ro !cb
14	Eg	0	1	0	0	0	0	1	0																							= digon	; rb !rp
15	Eh	0	1	0	0	0	0	0	1																							= digon	; rp !rb
16	Ei	0	0	0	0	0	1	1	0																							= digon	; cb !ro
17	Ej	0	0	1	0	0	0	0	1																							= digon	; op !wb
18	Ek	0	0	1	1	0	0	0	0																							= digon	; ol !wg
19	El	0	0	0	1	1	0	0	0																							= digon	; lg !wl
20	Em	0	0	0	0	1	1	0	0																							= digon	; gc !wo
21	En	0	0	0	0	0	1	0	1																							= digon	; cp !wr
22	3a	1	1	0	0	0	0	1	0	1	0	0	0	1	0	1	0	0	0	0	0	0	0									= triangle	; pink
23	3b	0	1	1	0	0	0	0	1	0	0	0	0	0	1	0	1	0	1	0	0	0	0									= triangle	; blue
24	3c	1	1	1	0	0	0	0	0	1	1	0	0	0	1	0	0	0	0	0	0	0	0									= triangle	; cyan
25	3d	1	0	1	1	0	0	0	0	0	1	1	0	0	0	0	0	0	0	1	0	0	0									= triangle	; green
26	3e	1	0	0	1	1	0	0	0	0	0	1	1	0	0	0	0	0	0	0	1	0	0									= triangle	; lime
27	4a	1	0	0	0	1	1	1	0	0	0	0	1	1	0	0	0	1	0	0	0	1	0									= square	; orange
28	4b	0	1	0	0	0	1	1	1	0	0	0	0	0	0	1	1	1	0	0	0	0	1									= square	; red
29	5a	0	0	1	1	1	1	0	1	0	0	0	0	0	0	0	0	0	1	1	1	1	1									= pentagon	; white
30	C1a	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	= triangulated pinched triangular cupola	;

Usage as facets

24× 1-facets of a (dual of triangular hebesphenorotundaeic rhombochoron)

Incidence matrix

Dual: (dual of triangular hebesphenorotundaeic rhombochoron)

#	TXID	Va	Vb	Vc	Vd	Ve	Ea	Eb	Ec	Ed	Ee	Ef	Eg	Eh	Ei	Ej	Ek	El	Em	En	3a	5a	3b	3c	4a	4b	3d	4c	3e	3f	3g	3h	3i	3j	3k	5b	3l	3m	6a	C1a	C2a	C3a	C4a	C5a	C5b	C5c	C6a	Type	Name
0	Va																																															= point	; red
1	Vb																																															= point	; orange
2	Vc																																															= point	; green
3	Vd																																															= point	; blue
4	Ve																																															= point	; purple
5	Ea	2	0	0	0	0																																										= digon	; rr
6	Eb	1	1	0	0	0																																										= digon	; ro
7	Ec	0	2	0	0	0																																										= digon	; oo horz
8	Ed	0	2	0	0	0																																										= digon	; oo vert
9	Ee	0	1	1	0	0																																										= digon	; og rad
10	Ef	0	1	1	0	0																																										= digon	; og orb
11	Eg	0	1	0	1	0																																										= digon	; ob rad
12	Eh	0	1	0	1	0																																										= digon	; ob orb
13	Ei	0	1	0	0	1																																										= digon	; op
14	Ej	0	0	2	0	0																																										= digon	; gg orange
15	Ek	0	0	2	0	0																																										= digon	; gg blue
16	El	0	0	1	1	0																																										= digon	; gb
17	Em	0	0	0	1	1																																										= digon	; bp
18	En	0	0	0	0	2																																										= digon	; pp
19	3a	3	0	0	0	0	3	0	0	0	0	0	0	0	0	0	0	0	0	0																												= triangle	; rrr
20	5a	2	2	0	1	0	1	2	0	0	0	0	0	2	0	0	0	0	0	0																												= pentagon	; rroob
21	3b	1	2	0	0	0	0	2	1	0	0	0	0	0	0	0	0	0	0	0																												= triangle	; roo horz
22	3c	1	2	0	0	0	0	2	0	1	0	0	0	0	0	0	0	0	0	0																												= triangle	; roo vert
23	4a	0	4	0	0	0	0	0	2	2	0	0	0	0	0	0	0	0	0	0																												= square	; oooo
24	4b	0	2	2	0	0	0	0	1	0	2	0	0	0	0	0	1	0	0	0																												= square	; oogg
25	3d	0	2	0	1	0	0	0	1	0	0	0	2	0	0	0	0	0	0	0																												= triangle	; oob
26	4c	0	2	0	0	2	0	0	1	0	0	0	0	0	2	0	0	0	0	1																												= square	; oopp
27	3e	0	2	1	0	0	0	0	0	1	2	0	0	0	0	0	0	0	0	0																												= triangle	; oog rad
28	3f	0	2	1	0	0	0	0	0	1	0	2	0	0	0	0	0	0	0	0																												= triangle	; oog orb
29	3g	0	1	2	0	0	0	0	0	0	1	1	0	0	0	1	0	0	0	0																												= triangle	; ogg
30	3h	0	1	1	1	0	0	0	0	0	1	0	1	0	0	0	0	1	0	0																												= triangle	; ogb rad
31	3i	0	1	1	1	0	0	0	0	0	0	1	0	1	0	0	0	1	0	0																												= triangle	; ogb orb
32	3j	0	1	0	1	1	0	0	0	0	0	0	1	0	1	0	0	0	1	0																												= triangle	; obp rad
33	3k	0	1	0	1	1	0	0	0	0	0	0	0	1	1	0	0	0	1	0																												= triangle	; obp orb
34	5b	0	0	2	2	1	0	0	0	0	0	0	0	0	0	1	0	2	2	0																												= pentagon	; ggbbp
35	3l	0	0	2	1	0	0	0	0	0	0	0	0	0	0	0	1	2	0	0																												= triangle	; ggb
36	3m	0	0	0	1	2	0	0	0	0	0	0	0	0	0	0	0	0	2	1																												= triangle	; bpp
37	6a	0	0	0	0	6	0	0	0	0	0	0	0	0	0	0	0	0	0	6																												= hexagon	; pppppp
38	C1a	3	6	0	3	6	3	6	3	0	0	0	0	6	6	0	0	0	6	6	1	3	3	0	0	0	0	3	0	0	0	0	0	0	6	0	0	3	1									= triangular hebesphenorotunda	;
39	C2a	2	4	2	2	0	1	4	0	2	0	4	0	4	0	0	1	4	0	0	0	2	0	2	0	0	0	0	0	2	0	0	4	0	0	0	2	0	0									= metabidiminished icosahedron	;
40	C3a	0	4	2	0	0	0	0	2	2	4	0	0	0	0	0	1	0	0	0	0	0	0	0	1	2	0	0	2	0	0	0	0	0	0	0	0	0	0									= triangular prism	;
41	C4a	0	1	2	2	1	0	0	0	0	1	1	1	1	1	1	0	2	2	0	0	0	0	0	0	0	0	0	0	0	1	1	1	1	1	1	0	0	0									= pentagonal pyramid	;
42	C5a	1	4	0	0	0	0	4	2	2	0	0	0	0	0	0	0	0	0	0	0	0	2	2	1	0	0	0	0	0	0	0	0	0	0	0	0	0	0									= square pyramid	; roooo
43	C5b	0	2	2	1	0	0	0	1	0	2	0	2	0	0	0	1	2	0	0	0	0	0	0	0	1	1	0	0	0	0	2	0	0	0	0	1	0	0									= square pyramid	; ooggb
44	C5c	0	2	0	1	2	0	0	1	0	0	0	2	0	2	0	0	0	2	1	0	0	0	0	0	0	1	1	0	0	0	0	0	2	0	0	0	1	0									= square pyramid	; oobpp
45	C6a	0	2	2	0	0	0	0	0	1	2	2	0	0	0	1	0	0	0	0	0	0	0	0	0	0	0	0	1	1	2	0	0	0	0	0	0	0	0									= tetrahedron	;
46	H4.1a	6	24	12	12	12	6	24	12	12	24	24	24	24	24	6	6	24	24	12	2	12	12	12	6	12	12	12	12	12	24	24	24	24	24	12	12	12	2	4	6	6	24	6	12	12	12	= triangular hebesphenorotundaeic rhombochoron	;

Usage as facets

This polytope does not currently appear as facets in any higher-dimensional polytopes in the database.

Triangulated pinched triangular cupola

Net space:	3
Bounding space:	3
Elements:	8, 14, 8
Symmetry group:	Unknown
SSCN:	Unknown
SSC2:	Unknown
Circular packing value:	Unknown
Square packing value:	Unknown