Knowledge (XXG)

Hemi-icosahedron

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328: 29: 248: 302: 398: 136: 228:, which could be topologically identical to the hemi-icosahedron if each of the 3 square faces were divided into two triangles. 428: 45: 209:
where opposite points along the boundary are connected and dividing the hemisphere into three equal parts.
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by 10 triangles), which can be visualized by constructing the projective plane as a
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which has a complete graph of edges, but only contains half of the (20) faces.
247: 353: 313: 267: 178: 63: 349: 385:; Schulte, Egon (December 2002), "6C. Projective Regular Polytopes", 326: 339:
represents the 6 vertices and 15 edges of the hemi-icosahedron
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It can be represented symmetrically on faces, and vertices as
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It has the same vertices and edges as the 5-dimensional
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It has 10 triangular faces, 15 edges, and 6 vertices.
389:(1st ed.), Cambridge University Press, pp.  283: 16:
Abstract regular polyhedron with 10 triangular faces
165: 153: 135: 116: 104: 89: 79: 69: 56: 41: 21: 296: 8: 27: 288: 282: 242: 18: 7: 356:constructed from 11 hemi-icosahedra. 220:It is also related to the nonconvex 14: 189:, containing half the faces of a 246: 1: 312:. With this embedding, the 187:abstract regular polyhedron 46:abstract regular polyhedron 445: 387:Abstract Regular Polytopes 273:From the point of view of 193:. It can be realized as a 26: 277:this is an embedding of 352:- an abstract regular 340: 308:with 6 vertices) on a 298: 330: 310:real projective plane 299: 297:{\displaystyle K_{6}} 262:The complete graph K6 203:real projective plane 195:projective polyhedron 51:projective polyhedron 429:Projective polyhedra 414:The hemi-icosahedron 281: 106:Vertex configuration 226:tetrahemihexahedron 191:regular icosahedron 341: 294: 222:uniform polyhedron 360:hemi-dodecahedron 322:hemi-dodecahedron 259: 258: 238:Schlegel diagrams 175: 174: 160:hemi-dodecahedron 436: 403: 303: 301: 300: 295: 293: 292: 250: 243: 183:hemi-icosahedron 148: 131: 124: 112: 100: 35:Schlegel diagram 31: 22:Hemi-icosahedron 19: 444: 443: 439: 438: 437: 435: 434: 433: 419: 418: 410: 401: 383:McMullen, Peter 381: 378: 370:hemi-octahedron 346: 338: 284: 279: 278: 264: 234: 215: 155:Dual polyhedron 146: 141: 130: 126: 122: 118:Schläfli symbol 110: 95: 48: 37: 17: 12: 11: 5: 442: 440: 432: 431: 421: 420: 417: 416: 409: 408:External links 406: 405: 404: 399: 377: 374: 373: 372: 367: 362: 357: 345: 342: 336: 333:complete graph 318:Petersen graph 306:complete graph 291: 287: 263: 260: 257: 256: 255:Face-centered 252: 251: 233: 230: 214: 211: 173: 172: 170:non-orientable 167: 163: 162: 157: 151: 150: 144: 139: 137:Symmetry group 133: 132: 128: 120: 114: 113: 108: 102: 101: 93: 87: 86: 83: 77: 76: 73: 67: 66: 60: 54: 53: 43: 39: 38: 32: 24: 23: 15: 13: 10: 9: 6: 4: 3: 2: 441: 430: 427: 426: 424: 415: 412: 411: 407: 402: 400:0-521-81496-0 396: 392: 388: 384: 380: 379: 375: 371: 368: 366: 363: 361: 358: 355: 351: 348: 347: 343: 334: 329: 325: 323: 319: 315: 311: 307: 289: 285: 276: 271: 269: 261: 254: 253: 249: 245: 244: 241: 239: 231: 229: 227: 223: 218: 212: 210: 208: 204: 200: 196: 192: 188: 184: 180: 171: 168: 164: 161: 158: 156: 152: 147: 140: 138: 134: 121: 119: 115: 109: 107: 103: 98: 94: 92: 88: 84: 82: 78: 74: 72: 68: 65: 61: 59: 55: 52: 47: 44: 40: 36: 30: 25: 20: 386: 275:graph theory 272: 265: 235: 219: 216: 199:tessellation 182: 176: 96: 91:Euler char. 376:References 354:4-polytope 314:dual graph 207:hemisphere 166:Properties 149:, order 60 33:decagonal 365:hemi-cube 268:5-simplex 111:3.3.3.3.3 64:triangles 49:globally 423:Category 344:See also 320:--- see 213:Geometry 179:geometry 81:Vertices 391:162–165 350:11-cell 316:is the 201:of the 123:{3,5}/2 397:  232:Graphs 224:, the 185:is an 97:χ 304:(the 127:{3,5} 71:Edges 58:Faces 395:ISBN 331:The 181:, a 42:Type 197:(a 177:In 125:or 99:= 1 62:10 425:: 393:, 324:. 240:: 75:15 337:6 335:K 290:6 286:K 145:5 143:A 129:5 85:6

Index


Schlegel diagram
abstract regular polyhedron
projective polyhedron
Faces
triangles
Edges
Vertices
Euler char.
Vertex configuration
Schläfli symbol
Symmetry group
A5
Dual polyhedron
hemi-dodecahedron
non-orientable
geometry
abstract regular polyhedron
regular icosahedron
projective polyhedron
tessellation
real projective plane
hemisphere
uniform polyhedron
tetrahemihexahedron
Schlegel diagrams

5-simplex
graph theory
complete graph

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