408:
919:
936:
927:
203:
264:
255:
81:
1317:
1310:
1303:
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892:
1075:
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1138:
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293:
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273:
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22:
1427:
Koch 1972 Koch, Elke, Wirkungsbereichspolyeder und
Wirkungsbereichsteilunger zukubischen Gitterkomplexen mit weniger als drei Freiheitsgraden (Efficiency Polyhedra, and Efficiency Dividers, cubic lattice complexes with less than three degrees of freedom) Dissertation, University Marburg/Lahn 1972 -
230:, except two edges from the original tetrahedron are reduced to zero length making pentagonal faces. The dual polyhedra can be called a skew-truncated tetragonal disphenoid, where 2 edges along the symmetry axis completely truncated down to the edge midpoint.
197:
If the space-filling polyhedron is placed in a 3-D coordinate grid, the coordinates for the 8 vertices can be given as: (0, ±2, −1), (±2, 0, 1), (±1, 0, −1), (0, ±1, 1).
40:
688:, with alternate cells removed and augmented into neighboring cells by a center vertex. The rhombic faces in the honeycomb are aligned along 3 orthogonal planes.
1247:
symmetry. These paired-cells stack more easily as inter-locking elements. Long sequences of these can be stacked together in 3 axes to fill space.
522:
460:
1236:
for its cross-sectional appearance. The two right-most symmetric projections below show the rhombi edge-on on the top, bottom and a middle
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189:(diamond-shaped) faces. He catalogued it in a 1982 paper as 10-II, the second in a list of 26 known space-filling decahedra.
997:
with 6 vertices, 10 edges, and 6 faces (4 triangles, 2 right trapezoids). Michael
Goldberg identifies this polyhedron as an
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407:
986:
with 6 vertices, 11 edges, and 7 faces (6 triangles and 1 trapezoid). Michael
Goldberg identifies this polyhedron as a
896:
355:
1331:
568:
170:
1255:
959:
cross-section between the two rhombic faces. It is a decahedron with 12 vertices, 20 edges, and 10 faces (4
918:
935:
1384:
926:
1403:
640:
600:
306:
227:
202:
222:
symmetry, which projects as order-4 dihedral (square) symmetry in two dimensions. It can be seen as a
442:
263:
254:
900:
277:
223:
181:
because its faces are not composed entirely of regular polygons. Michael
Goldberg named it after a
80:
975:). Michael Goldberg labels this polyhedron 10-XXV, the 25th in a list of space-filling decahedra.
433:
174:
1316:
1309:
1302:
1295:
1074:
1060:
341:
1288:
1137:
1173:
1086:
993:
It can be further dissected as a quarter-model by another symmetry plane into a space-filling
891:
116:
1215:
1207:
1067:
437:
292:
283:
226:, with two pairs of coplanar triangles merged into rhombic faces. The dual is similar to a
1163:
1145:
1100:
1093:
481:
142:
106:
88:
1416:
1401:
1382:
907:
173:
with 10 faces, 2 opposite rhombi with orthogonal major axes, connected by 8 identical
1435:
604:
178:
272:
1240:
where the two halves are connected. The 2D projections can look convex or concave.
418:
182:
983:
608:
429:
422:
1243:
It has 12 vertices, 28 edges, and 18 faces (16 triangles and 2 rhombi) within D
994:
1355:
1251:
964:
301:
982:
can be dissected as a half-model on a symmetry plane into a space-filling
1151:
960:
162:
94:
972:
968:
956:
186:
1156:
99:
332:
990:, type 7-XXIV, the 24th in a list of space-fillering heptahedra.
1381:
Geometriae
Dedicata, June 1978, Volume 7, Issue 2, pp 175–184
15:
1001:, type 6-X, the 10th in a list of space-filling hexahedron.
940:
Honeycomb structure orthogonally viewed along cubic plane
1400:
Geom. Dedicata, June 1977, Volume 6, Issue 1, pp 99–108
36:
1258:
on the rhombi can be done with 2 unit translation in
1272:
1003:
690:
232:
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1172:
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1144:
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151:
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125:
115:
105:
87:
73:
31:
may be too technical for most readers to understand
1417:Bowties: A Novel Class of Space Filling Polyhedron
1354:. Structural Topology, 1982, num. Type 10-II
185:, as a 10-faced polyhedron with two opposite
8:
922:Dual honeycomb of icosahedra and tetrahedra
335:
1214:
1136:
1005:Dissected models in symmetric projections
177:faces. Although it is convex, it is not a
79:
1269:(±1/2, 0, −1), (0, ±1/2, 0), (±1/2, 0, 1)
251:
59:Learn how and when to remove this message
43:, without removing the technical details.
1343:
1127:
646:Cells can be seen as the cells of the
565:alternated bitruncated cubic honeycomb
523:alternated bitruncated cubic honeycomb
461:Alternated bitruncated cubic honeycomb
70:
41:make it understandable to non-experts
7:
1274:Bow-tie model (two ten-of-diamonds)
1266:(0, ±1, −1), (±1, 0, 0), (0, ±1, 1),
988:triply truncated quadrilateral prism
607:of this honeycomb are their duals –
147:Skew-truncated tetragonal disphenoid
14:
1250:The 12 vertex coordinates in a 2-
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1379:On the space-filling heptahedra
1228:can be attached as a nonconvex
999:ungulated quadrilateral pyramid
947:Related space-filling polyhedra
913:tetragonal disphenoid honeycomb
648:tetragonal disphenoid honeycomb
466:
456:
428:
414:
400:
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340:
1398:On the space-filling hexahedra
1352:On the Space-filling Decahedra
480:is used in the honeycomb with
1:
1285:
1106:
1080:
1054:
1028:
1008:
311:
1415:Robert Reid, Anthony Steed
897:Bitruncated cubic honeycomb
1458:
1366:On Space-filling Decahedra
931:Ten-of-diamonds honeycomb
888:
336:Ten-of-diamonds honeycomb
167:ten-of-diamonds decahedron
74:Ten-of-diamonds decahedron
1332:Elongated gyrobifastigium
1281:
1213:
1135:
842:
702:
318:
312:
244:
238:
78:
171:space-filling polyhedron
1442:Space-filling polyhedra
1232:space-filler, called a
955:can be dissected in an
601:tetragonal disphenoidal
569:pyritohedral icosahedra
521:, being the dual of an
641:tetragonal disphenoids
1428:Model 10/8–1, 28–404.
307:Truncated tetrahedron
234:Symmetric projection
228:truncated tetrahedron
901:truncated octahedral
1350:Goldberg, Michael.
1275:
1006:
278:triakis tetrahedron
235:
224:triakis tetrahedron
1396:Goldberg, Michael
1377:Goldberg, Michael
1273:
1004:
233:
175:isosceles triangle
1323:
1322:
1222:
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1121:
1120:
1111:v=12, e=20, f=10
944:
943:
474:
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326:
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159:
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69:
68:
61:
1449:
1420:
1413:
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1375:
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973:isotoxal octagon
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703:Dual alternated
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470:Cell-transitive
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375:
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370:
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365:
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333:
322:v=12, e=18, f=8
319:v=10, e=16, f=8
316:v=8, e=18, f=12
313:v=8, e=16, f=10
304:
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239:Ten of diamonds
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83:
71:
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24:
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1226:ten-of-diamonds
1192:
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1126:
1117:v=6, e=10, f=6
1114:v=6, e=11, f=7
1050:
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1024:
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980:ten-of-diamonds
953:ten-of-diamonds
949:
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567:fills space by
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496:
491:
486:
484:
482:Coxeter diagram
478:ten-of-diamonds
451:
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405:
404:Ten-of-diamonds
392:
387:
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356:Coxeter diagram
349:
342:Schläfli symbol
331:
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216:ten-of-diamonds
212:
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143:Dual polyhedron
135:
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37:help improve it
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1368:, type 10-XXV.
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1234:rhombic bowtie
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1184:Symmetry group
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1131:Rhombic bowtie
1125:
1124:Rhombic bowtie
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1025:quarter model
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605:vertex figures
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415:Vertex figures
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127:Symmetry group
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1256:augmentations
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1212:
1209:
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1202:space-filling
1201:
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179:Johnson solid
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155:space-filling
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29:This article
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998:
992:
987:
979:
977:
952:
950:
645:
603:tetrahedra,
564:
563:. Since the
477:
475:
419:dodecahedron
288:Solid faces
259:Solid faces
215:
213:
196:
183:playing card
166:
160:
55:
46:
30:
1387:type 7-XXIV
1254:. (further
1020:half model
1018:Heptahedral
1015:half model
984:heptahedron
700:Alternated
609:pyritohedra
423:tetrahedron
193:Coordinates
1338:References
1282:Symmetric
1199:Properties
1051:, order 2
1044:, order 2
1037:, order 4
1023:Hexahedral
1013:Decahedral
995:hexahedron
965:trapezoids
467:Properties
152:Properties
49:April 2017
1252:unit cube
1224:Pairs of
1194:, order 8
1152:triangles
1108:Elements
1030:Symmetry
1010:Relation
961:triangles
957:octagonal
434:Fibrifold
329:Honeycomb
137:, order 8
95:triangles
1436:Category
1406:type 6-X
1326:See also
1174:Vertices
971:, and 1
885:{4,3,4}
840:{4,3,4}
795:{4,3,4}
750:{4,3,4}
694:Uniform
350:{4,3,4}
248:Related
242:Related
210:Symmetry
163:geometry
117:Vertices
1230:bow-tie
969:rhombus
438:Coxeter
187:rhombic
35:Please
1157:rhombi
1056:Edges
903:cells
599:, and
297:Edges
268:Edges
165:, the
100:rhombi
1164:Edges
1146:Faces
697:Dual
447:(204)
430:Space
245:Dual
218:has D
169:is a
107:Edges
89:Faces
1419:2003
1279:Skew
1238:neck
1082:Net
978:The
967:, 1
963:, 4
951:The
639:and
476:The
457:Dual
401:Cell
214:The
1404:PDF
1385:PDF
1262:.)
1208:Net
1150:16
899:of
883:1,2
881:dht
838:1,2
793:1,2
748:1,2
348:1,2
346:dht
161:In
39:to
1438::
1245:2h
1191:2h
1178:12
1168:28
1155:2
1035:2v
836:ht
791:dt
650:,
643:.
611:,
571:,
525:,
452:]
220:2d
134:2d
111:16
98:2
93:8
1260:z
1189:D
1049:2
1047:C
1042:s
1040:C
1033:C
746:t
450:8
445:3
443:I
132:D
121:8
62:)
56:(
51:)
47:(
33:.
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