D4.7 (EntityTopic, 15)

From Hi.gher. Space

D4.7 is a bilbirothawroid discovered by student91 on February 24, 2014. It is based on a modified tristratic cap derived from the rectified 600-cell o5o3x3o.

The modified tristratic cap has the structure o5x3o || x5o3x || o5o3F || o5x3x. This crown jewel is then constructed from this tristratic cap by deleting the vertices of 8 triangles from the x5o3x layer that lie at the vertices of an inscribed cube.

Its faces are 308 triangles, 42 squares, 48 pentagons and 20 hexagons. Its cells are 12+12+24 = 48 tetrahedra, 6 triangular prisms, 6 square pyramids, 12 pentagonal pyramids, 12 triangular cupolae, 12 octahedra, 12 tridiminished icosahedra, 8 triangular hebesphenorotundae, a rhodomesohedron and a truncated icosahedron - a total of ten different cell types!

It is the first crown jewel to be discovered with (a 4D variant of) pyritohedral symmetry.

Projections

Centered on icosidodecahedron:

(image)

Vertex types highlighted:

(image)

Incidence matrix

Dual: D4.7 dual

#TXIDVaVbVcVdVeVfVgVhEaEbEcEdEeEfEgEhEiEjEkElEmEnEoEpEqErEsEtEuEv3a3b3c3d3e3f3g5a3h5b6a6b4a3i4b3j4c3k3l3m3n3o3p3q5c3rC1aC1bC1cC2aC3aC4aC5aC6aC7aC8aC9aC10aTypeName
0 Va = point ; red
1 Vb = point ; orange
2 Vc = point ; yellow
3 Vd = point ; green
4 Ve = point ; cyan
5 Vf = point ; blue
6 Vg = point ; purple
7 Vh = point ; slate
8 Ea 11000000 = digon ; ro
9 Eb 10100000 = digon ; ry
10 Ec 10010000 = digon ; rg
11 Ed 10001000 = digon ; rc
12 Ee 10000100 = digon ; rb
13 Ef 02000000 = digon ; oo
14 Eg 01100000 = digon ; oy pen
15 Eh 01100000 = digon ; oy hex
16 Ei 01000100 = digon ; ob
17 Ej 00110000 = digon ; yg
18 Ek 00101000 = digon ; yc
19 El 00020000 = digon ; gg
20 Em 00011000 = digon ; gc
21 En 00002000 = digon ; cc parl
22 Eo 00002000 = digon ; cc perp
23 Ep 00001100 = digon ; cb
24 Eq 00001010 = digon ; cp
25 Er 00001001 = digon ; cs
26 Es 00000110 = digon ; bp
27 Et 00000020 = digon ; pp orb
28 Eu 00000020 = digon ; pp rad
29 Ev 00000011 = digon ; ps
30 3a 120000002000010000000000000000 = triangle ; roo
31 3b 111000001100001000000000000000 = triangle ; roy
32 3c 110001001000100010000000000000 = triangle ; rob
33 3d 101100000110000001000000000000 = triangle ; ryg
34 3e 101010000101000000100000000000 = triangle ; ryc
35 3f 100110000011000000001000000000 = triangle ; rgc
36 3g 100020000002000000000010000000 = triangle ; rcc
37 5a 100011200001100000000000101010 = pentagon ; rcbpp
38 3h 020001000000010020000000000000 = triangle ; oob
39 5b 022100000000012002000000000000 = pentagon ; ooyyg
40 6a 022200000000010202010000000000 = hexagon ; ooyygg
41 6b 033000000000003300000000000000 = hexagon ; oyoyoy
42 4a 011011000000000110100001000000 = square ; oycb
43 3i 001110000000000001101000000000 = triangle ; ygc
44 4b 000220000000000000012100000000 = square ; ggcc
45 3j 000120000000000000002010000000 = triangle ; gcc
46 4c 000040000000000000000220000000 = square ; cccc
47 3k 000021000000000000000102000000 = triangle ; ccb
48 3l 000020010000000000000100020000 = triangle ; ccs parl
49 3m 000020010000000000000010020000 = triangle ; ccs perp
50 3n 000011100000000000000001101000 = triangle ; cbp
51 3o 000010110000000000000000110001 = triangle ; cps
52 3p 000001200000000000000000002100 = triangle ; bpp
53 3q 000000300000000000000000000030 = triangle ; ppp
54 5c 000000410000000000000000000122 = pentagon ; pppps
55 3r 000000210000000000000000000102 = triangle ; pps
56 C1a 12000100200011002000000000000010200000100000000000000000 = tetrahedron ; roob
57 C1b 10012000001200000000201000000000000210000000010000000000 = tetrahedron ; rgcc
58 C1c 10111000011100000110100000000000011100000001000000000000 = tetrahedron ; rygc
59 C2a 00024000000000000001422000000000000000000000221000000000 = triangular prism ;
60 C3a 00004001000000000000022004000000000000000000001022000000 = square pyramid ;
61 C4a 12210000221001200200000000000012020000010000000000000000 = pentagonal pyramid ;
62 C5a 02222100000001022221210200000000000000101022100100000000 = triangular cupola ;
63 C6a 00002121000000000000010222210200000000000000000110221001 = octahedron ;
64 C7a 10002141000210000000001022212200000012000000000001021010 = tridiminished icosahedron ;
65 C8a 33303330330330333030000330303003303003000130000000300100 = triangular hebesphenorotunda ;
66 C9a 00000024600000000000000000001224240000000000000000000000081212 = rhodomesohedron ;
67 C10a 02424120000000001224240240600000000000000000001212800000000000000 = truncated icosahedron ;
68 H4.1a 122424122412246242412241212242424242462412122424242412242412242424242412241212128242412126121212242412812121212246612121212811 = D4.7 ;

Usage as facets

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

Software models

Retrieved from "http://hi.gher.space/wiki/D4.7"